Unit 8 quadratic equations homework 14 projectile motion

1 Quadratic Equations UNIT BUNDLE!

2 Quadratic Equations: Sample Unit Outline DAY 1 TOPIC Intro to Quadratic Equations: Axis of Symmetric, Vertex, Minimum, Maximum, Parabolas HOMEWORK HW #1 DAY 2 Graphing Quadratic Equations HW #2 DAY 3 Quadratic Roots HW #3 DAY 4 Quiz 8-1 None DAY 5 Solving Quadratics by Factoring (Day 1) HW #4 DAY 6 Solving Quadratics by Factoring (Day 2) HW #5 DAY 7 Review Solving Quadratics by Factoring Study DAY 8 Quiz 8-2 None DAY 9 The Quadratic Formula HW #6 DAY 10 Factoring vs. Quadratic Formula: Selecting the best method. HW #7 DAY 11 Solving Quadratics by Square Roots Method (ax 2 + c = 0) HW #8 DAY 12 Review: Solving Quadratics by all Methods HW #9 DAY 13 DAY 14 DAY 15 DAY 16 Quiz 8-3 Area Problems; Start Projectile Motion Projectile Motion Linear vs. Quadratic Models None HW #10 HW #11 DAY 17 Quadratic Inequalities HW #12 DAY 18 Unit Review; Complete Study Guide Study DAY 19 TEST None See sample images of the pages on the next page.

3 Name: Class: Topic: Date: Main Ideas/Questions Standard Form Graph Types Of Parabolas Notes All quadratic equations are written in the form: When graphed, a quadratic equation creates a U-shaped curve called a. Use your graphing calculator to sketch the following: y = x 2 + 2x 5 y = -x 2 + 3x + 7 If a is, then the parabola opens, like a smile If a is, then the parabola opens, like a frown Axis of Symmetry Formula for the axis of symmetry: Vertex When the vertex is the lowest point, it is called a. When the vertex is the highest point, it is called a. Examples 1. y = x 2 + 8x + 15 Axis of Symmetry: Vertex: Sketch: Gina Wilson, 2013

4 2. y = -x x 23 Axis of Symmetry: Vertex: Sketch: 3. y = 3x 2 12x + 5 Axis of Symmetry: Vertex: Sketch: 4. y = 4x 2 + 8x 1 Axis of Symmetry: Vertex: Sketch: 5. y = -x 2 4x 2 Axis of Symmetry: Vertex: Sketch: 6. y = 2x 2 12x + 9 Axis of Symmetry: Vertex: Sketch: 7. y = -3x 2 24x 42 Axis of Symmetry: Vertex: Sketch: 8. y = -x 2 + 4x Axis of Symmetry: Vertex: Sketch: 9. y = x 2 3 Axis of Symmetry: Vertex: Sketch: 10. y = -2x Axis of Symmetry: Vertex: Sketch: Gina Wilson, 2013

5 Name: Date: Bell: Unit 8: Quadratic Equations Homework 1: Intro to Quadratics Complete the following statements. ** This is a 2-page document! ** 1. The standard form of a quadratic equation is. 2. The curve formed by a quadratic equation is called a. 3. The formula for the axis of symmetry is. 4. If the vertex is the highest point on the graph, it is called a. 5. If a vertex is the lowest point on a graph, it is called a. Find the axis of symmetry and vertex for the following quadratic equations. Then, sketch the parabola and label all parts. 6. y = x 2 + 6x + 4 Axis of Symmetry: Vertex: Sketch: 7. y = -2x 2 + 8x 5 Axis of Symmetry: Vertex: Sketch: 8. y = x 2 2x Axis of Symmetry: Vertex: Sketch: 9. y = -x 2 8x 9 Axis of Symmetry: Vertex: Sketch: Gina Wilson, 2013

6 10. y = -5x 2 20x 26 Axis of Symmetry: Vertex: Sketch: 11. y = x 2 4 Axis of Symmetry: Vertex: Sketch: 12. y = -x 2 + 2x 4 Axis of Symmetry: Vertex: Sketch: 13. y = -3x 2 Axis of Symmetry: Vertex: Sketch: 14. y = 2x 2 12x + 10 Axis of Symmetry: Vertex: Sketch: 15. y = x 2 +10x + 24 Axis of Symmetry: Vertex: Sketch: Gina Wilson, 2013

7 GRAPHING QUADRATIC EQUATIONS y = ax 2 + bx + c Steps to graph a quadratic equation : Step 1: Find the axis of symmetry. Step 2: Find the vertex. Step 3: Fill in a table of values using your calculator. Step 4: Graph! Practice! Graph each quadratic equation. 1. y = x 2 Axis of Symmetry: x y Vertex: Domain: Range: 2. y = x 2 + 2x + 5 Axis of Symmetry: x y Vertex: Domain: Range: 3. y = -x 2 8x 17 Axis of Symmetry: x y Vertex: Domain: Range: Gina Wilson, 2013

8 4. y = -2x 2 + 4x + 1 Axis of Symmetry: x y Vertex: Domain: Range: 5. y = x 2 6x + 13 Axis of Symmetry: x y Vertex: Domain: Range: 6. y = -x 2 4 Axis of Symmetry: x y Vertex: Domain: Range: 7. y = 2x 2 + 8x Axis of Symmetry: Vertex: x y Domain: Range: Gina Wilson, 2013

9 8. y = -x 2 + 4x + 3 Axis of Symmetry: x y Vertex: Domain: Range: 9. y = -x 2 2x Axis of Symmetry: Vertex: x y Domain: Range: 10. y = -3x 2 18x 20 Axis of Symmetry: Vertex: x y Domain: Range: Gina Wilson, 2013

10 Analyzing Quadratic Graphs GRAPH A GRAPH B Answer the questions given the graphs above. 1. What is the axis of symmetry for Graph A? 2. What is the axis of symmetry for Graph B? 3. What is the vertex of Graph A? Maximum or Minimum? 4. What is the vertex of Graph B? Maximum or Minimum? 5. Identify the domain and range of Graph A. 6. Identify the domain and range of Graph B. 7. Identify the equation for Graph A: A. y = x 2 4x 1 C. y = -x 2 4x 1 B. y = x 2 + 4x 1 D. y = -x 2 + 4x 1 8. Identify the equation for Graph B: A. y = x 2 6x 5 C. y = -x 2 6x 5 B. y = x 2 + 6x 5 D. y = -x 2 + 6x 5 Gina Wilson, 2013

11 Name: Date: Bell: Unit 8: Quadratic Equations Homework 2: Graphing Quadratic Equations Graph each quadratic equation by making a table. 1. y = x x + 26 ** This is a 2-page document! ** Axis of Symmetry: Vertex: Domain: x y Range: 2. y = -2x 2 + 8x Axis of Symmetry: Vertex: Domain: x y Range: 3. y = x 2 2x Axis of Symmetry: Vertex: Domain: x y Range: 4. y = -x 2 8x 16 Axis of Symmetry: Vertex: Domain: x y Range: Gina Wilson, 2013

12 5. y = 3x 2 5 Axis of Symmetry: Vertex: Domain: x y Range: 6. y = -2x x 15 Axis of Symmetry: Vertex: Domain: x y Range: 7. y = -x Axis of Symmetry: Vertex: Domain: x y Range: 8. y = 2x 2 16x + 30 Axis of Symmetry: Vertex: Domain: x y Range: Gina Wilson, 2013

13 Name: Class: Topic: Date: Main Ideas/Questions Notes Definition Also called,, Number of 2 SOLUTIONS 1 SOLUTION NO SOLUTION Solutions Examples 1. y = x 2 + 4x 5 x y Find the solutions of the following quadratics by graphing. Solutions: y = x 2 2x + 1 x y y = -x 2 + 2x 3 x y Gina Wilson, 2013

14 Solutions: 4. y = x 2 10x + 16 x y y = -x x y 6. y = -3x 2 + 6x x y The Discriminant Formula: If d > 0, then there are solutions. If d = 0, then there are solutions. If d < 0, then there are solutions. Examples Use the discriminant to determine the number of solutions. 7. y = x 2 + 5x y = x 2 3x y = x x y = 2x 2 4x y = 4x 2 12x y = -3x 2 + 5x 8 Gina Wilson, 2013

15 Name: Unit 8: Quadratic Equations Date: Bell: Homework 3: Quadratic Roots ** This is a 2-page document! ** 1. The points at which a quadratic equation intersects the x-axis are referred to as: Graph the quadratic equation and identify the solution(s). 2. y = x 2 + 2x 3 3. y = x 2 8x + 12 x y x y Solutions: Solutions: 4. y = x y = -x x 21 x y x y Solutions: Solutions: 6. y = x 2 4x y = -2x 2 8x x y x y Solutions: Solutions: Gina Wilson, 2013

16 8. y = x 2 6x y = x 2 + 4x + 9 x y x y Solutions: Solutions: Use the discriminant to determine the number of solutions. 10. y = x 2 3x y = 2x 2 4x y = -3x 2 + 5x y = x 2 5x y = -x 2 + 2x y = 4x 2 9 Gina Wilson, 2013

17 Entrance Ticket Name: Graph the quadratic equation by completing a table of values. Then, fill in the blanks. 1) y = -x 2 6x 5 x y Axis of Symmetry: Vertex: Domain: Range: Zeros: TURN OVER! Entrance Ticket Name: Graph the quadratic equations by completing a table of values. Then, fill in the blanks. 1) y = -x 2 6x 5 x y Axis of Symmetry: Vertex: Domain: Range: Zeros: TURN OVER!

18 2) y = x 2 + 4x + 4 x y Axis of Symmetry: Vertex: Domain: Range: Zeros: 2) y = x 2 + 4x + 4 x y Axis of Symmetry: Vertex: Domain: Range: Zeros:

19 Name: Date: Bell: Algebra I Honors Unit 8: Quadratic Equations Quiz 8-1: Graphing Quadratic Equations Match the following. 1. The standard form of a quadratic equation. 2. The U-shaped curve created by a quadratic equation. 3. The vertical line that divides the parabola into two equal parts. 4. The formula for the axis of symmetry. 5. The turning point of a parabola. 6. A vertex that is the highest point. A. d = b 2 4ac B. Minimum C. Axis of Symmetry D. y = ax 2 + bx + c E. Parabola F. Vertex 7. A vertex that is the lowest point. G. x = b 2a 8. The points at which the parabola intersects the x-axis. 9. Used to determine the number of solutions of a quadratic equation. 10. The formula for the Discriminant. H. Maximum I. Roots J. Discriminant Find the axis of symmetry and vertex for the following quadratic equations: 11. y = -x 2 2x 8 Axis of Symmetry: Vertex: 12. y = 2x Axis of Symmetry: Vertex: Fill in the blanks given the following graphs. 13. Axis of Symmetry: Vertex: Domain: Range: Zeros: Equation: A. y = x 2 + 6x 5 C. y = -x 2 + 6x 5 B. y = x 2 6x 5 D. y = -x 2 6x 5 Gina Wilson, 2013

20 14. Axis of Symmetry: Vertex: Domain: Range: Zeros: Equation: A. y = x 2 + 2x + 1 C. y = x 2 2x + 1 B. y = -x 2 + 2x + 1 D. y = -x 2 2x Axis of Symmetry: Vertex: Domain: Range: Zeros: Equation: A. y = x 2 + 8x 17 C. y = x 2 8x 17 B. y = -x 2 + 8x 17 D. y = -x 2 8x Axis of Symmetry: Vertex: Domain: Range: Zeros: Equation: A. y = x 2 4x C. y = x 2 + 4x B. y = x 2 4 D. y = x Use the Discriminant to determine the number of solutions. 17. y = x 2 10x y = -3x 2 + 7x y = -x y = 2x 2 + 9x 2 1 Gina Wilson, 2013

21 Quadratic Equations in Vertex Form What is vertex form? y = a(x h) 2 + k where (h, k) is the vertex of the parabola. How do we convert this back to standard form standard form? Use! 1. =( 2) +3 Axis of Symmetry: x y Vertex: Domain: Range: 2. =2( +3) 1 Axis of Symmetry: x y Vertex: Domain: Range: 3. = ( 2) +1 Axis of Symmetry: x y Vertex: Domain: Range: Gina Wilson, 2013

22 Solving Quadratics by Factoring Objective: To find quadratic solutions (roots, zeros, etc) by factoring, rather than graphing. Example: Find the solutions of the equation = + by factoring. Step 1: Set the quadratic equation equal to 0. Step 2: Factor the left side. Step 3: Set each factor e to equal to 0 and solve for x. Step 4: Write your answer using curly braces. Your Turn! Solve the quadratics by factoring. 1. x 2 + 4x + 3 = 0 2. x x + 24 = 0 3. x 2 + x 2 = 0 4. x 2 + 6x 27 = 0 5. x 2 10x + 21 = 0 6. x 2 x 20 = 0 7. x x + 25 = 0 8. x 2 8x + 16 = 0 9. x 2 8x = x x = 0 Gina Wilson, 2013

23 11. 6x 2 12x = x 2 6x = x 2 64 = x 2 25 = x 2 81 = x 2 49 = 0 Equations NOT in Standard Form orm You must MOVE-FACTOR-SOLVE! 17. x 2 + 4x = x 2 45 = 4x 19. x 2 5x 64 = 7x 20. x 2 10x + 49 = 4x x 2 = 28x x 2 = x 2 + 8x 23. x 2 = x 2 = 9 Gina Wilson, 2013

24 Name: Unit 8: Quadratic Equations Date: Bell: ** This is a 2-page document! ** Solve each quadratic equation by factoring. 1. x 2 + 7x + 12 = 0 2. x 2 8x 9 = 0 Homework 4: Solving Quadratics by Factoring (Day 1) 3. x 2 x 30 = 0 4. x 2 8x = x 2 10 = 9x 6. x x = x x 2 3x + 16 = 7x 8. x 2 + 3x 5 = x 2 x 46 = 3x x 2 14x 18 = -8x 2 Gina Wilson, 2013

25 11. 2x 2 7x + 4 = x x 2 + 3x = x x = x 2 3x = x 2 = 36x 16. x 2 36 = x 2 49 = x 2 = 1 Gina Wilson, 2013

26 SOLVING QUADRATICS BY FACTORING Day 2 Slip & Slide IMPORTANT: If you can factor out a by GCF, DO NOT use Slip & Slide! Example 1: Example 2: 3x 2 + 9x 12 = 0 5x 2 20x 60 = 0 Example 3: Example 4: 2x 2 + 3x 5 = 0 8x 2 22x + 5 = 0 Now you try! 1. 2x x + 8 = x 2 24x 28 = x x 10 = x 2 8x + 3 = 0 Gina Wilson, 2013

27 5. 3x x + 15 = x x 7 = x 2 21x + 4 = x 2 + 5x + 1 = x 2 8x 5 = x x + 9 = x 2 + 7x = x = 10x x x = x 2 + 7x = x Gina Wilson, 2013

28 Name: Unit 8: Quadratic Equations Date: Bell: ** This is a 2-page document! ** Solve each quadratic equation by factoring. 1. 2x 2 8x 24 = x 2 + 5x 30 = 0 Homework 5: Solving Quadratics by Factoring (Day 2) 3. 4x x + 8 = x 2 15x + 12 = x 2 7x 6 = x 2 + 5x + 3 = x 2 19x 5 = x 2 x 2 = 0 Gina Wilson, 2013

29 9. 6x 2 + 7x + 2 = x 2 11x + 2 = x 2 14x = x = 11x x = 5x x + 11 = -6x x 2 = 17x = 12x 4x 2 Gina Wilson, 2013

30 Name: Date: Bell: Algebra I Honors Unit 8: Quadratic Equations Solve the following quadratics by factoring. Quiz 8-2: Solving Quadratics by Factoring = =0 Answers = = = = = = = =24 B = =25 Bonus: Solve the quadratic equation + = Gina Wilson, 2013

31 Writing Quadratic Equations by Identifying the Roots! 1 y = ( )( ) 2 y = ( )( ) 3 y = ( )( ) 4 y = ( )( ) Gina Wilson, 2013

32 The Quadratic Formula = ± Some problems cannot be solved by factoring. The quadratic formula can be used in this situation to find the quadratic roots. Example: Solve x 2 6x + 4 = 0 by the quadratic formula. More Practice! 1. x x 2 = 0 2. x 2 11 = 4x 3. x 2 8x = x 2 5x 36 = 0 5. x 2 + 6x + 10 = x 2 12x 18 = 0 Gina Wilson, 2013

33 7. -x 2 + 7x 3 = 0 8. x 2 + 4x + 1 = x = 7 x x x = x 2 + 5x + 4 = x 2 + 7x 9 = x 2 8 = x = 12x 15. 3x 2 1 = -8x 16. 3x 2 + 7x = x 2 2x + 15 Gina Wilson, 2013

34 Name: Date: Bell: Unit 8: Quadratic Equations Homework 6: Solving Quadratics by The Quadratic Formula ** This is a 2-page document! ** Solve each quadratic equation by the quadratic formula. 1. x 2 + 4x 3 = x = 9x = ± 3. x 2 = -5x x 2 3x + 1 = 6 5. x 2 + 4x + 17 = 8 2x 6. 4x 2 6x 1 = 0 Gina Wilson, 2013

35 7. 5x 2 3x 1 = x 2 + 7x 18 = x 2 25 = x 2 7x 4 = x 2 4x 11. 8x 2 5 = -4x 12. 4x 2 18x = 0 Gina Wilson, 2013

36 Factoring vs. Quadratic Formula It is much more efficient to use factoring when possible, although the quadratic formula will work in all cases. Choose the most appropriate method to solve the following quadratic equations: =0 2 4 = = = = =0 7 42= = = =21 Gina Wilson, 2013

37 = = = = = = = = = =3 12 Gina Wilson, 2013

38 Name: Date: Bell: Unit 8: Quadratic Equations Homework 7: Solving Quadratics Review Factoring/Quadratic Formula ** This is a 2-page document! ** Use factoring or the Quadratic Formula to solve the following. 1. x 2 8x 20 = x 2 15x = x 2 25 = 0 4. x 2 8x 2 = 0 5. x 2 + 3x 40 = 0 6. x 2 15 = 0 7. x = 14x 8. 3x 2 + x 1 = 0 Gina Wilson, 2013

39 9. 18x 2 = 24x 10. x 2 7x + 12 = 3x x 2 11x + 28 = x 2 1 = 3x 2 + 9x 13. x 2 5 = x 2 5x = x 2 = x 2 1 = 5 3 Gina Wilson, 2013

40 Solving Quadratics: Square Roots Method Today we will solve quadratics using square roots. This method only works when there is no x term. + = Steps Step 1: Isolate x 2 = Step 2: Take the SQUARE ROOT of both sides Directions: Use the Square Roots Method to solve each quadratic equation: 1. 16= = = = =4 6. 5= = = = = = = 16 Gina Wilson, 2013

41 = = = = = =8 19. = = = = = = = =7 27. ( 17)= = = =46 What time is it? Gina Wilson, 2013

42 Name: Unit 8: Quadratic Equations Date: Bell: Homework 8: Solving Quadratics by Square Roots ** This is a 2-page document! ** Solve each quadratic equation by the square roots method. 1. x 2 49 = x 2 18 = x 2 20 = 0 4. x = 0 5. x 2 24 = x 2 22 = x = 8. 1 x 2 1 = x 2 25 = x 2 = 49 Gina Wilson, 2013

43 11. 81x 2 = x 2 7 = x = x 2 3 = x 2 6 = x 2 = x 2 92 = x 2 15 = x = x = x = 22. x = Gina Wilson, 2013

44 Group Members: Bell: REVIEW: Solving Quadratic Equations Work through each problem with your group members. Each person of the group should be participating and writing on their own paper. Factorin g: = = = =0 Squa re R oots: 5. = = = =16 The quadratic Form ula: = =0 Gina Wilson, 2013

45 = =3 YOUR CH OICE! = = = = = = = =4 +7 Gina Wilson, 2013

46 Name: Date: Bell: Unit 8: Quadratic Equations Homework 9: Solving Quadratics Review (All Methods) ** This is a 2-page document! ** Use factoring, square roots method, or the Quadratic Formula to solve the following. 1. x 2 8x 20 = x 2 15x = x 2 25 = 0 4. x 2 8x 2 = 0 5. x 2 + 3x 40 = 0 6. x 2 15 = 0 7. x = 14x 8. 3x 2 + x 1 = 0 Gina Wilson, 2013

47 9. 18x 2 = 24x 10. x 2 7x + 12 = 3x x 2 11x + 28 = x 2 1 = 3x 2 + 9x 13. x 2 5 = x 2 5x = x 2 = x 2 1 = 5 3 Gina Wilson, 2013

48 Name: Date: Bell: Algebra I Honors Unit 8: Quadratic Equations Quiz 8-3: Solving Quadratics Equations (All Methods) SOLVE BY FACTORING, SQUARE ROOTS, or QUADRATIC FORMULA 1. x 2 6x + 5 = 0 2. x 2 10x = 4 = ± Answers x 2 = x 2 3x 18 = x x 2 = 9x x 2 + 3x = x 2 14x = 0 x 2 8 = x x = 5x x 2 11 = 84 Gina Wilson, 2013

49 Quadratic Equation Area Problems! 1 Given the diagram below, find the value of x if the area of the rectangle is 78 square meters. 2 Given the diagram below, find the dimensions of the rectangle if the area of the rectangle is 108 square meters. x x 3 x + 7 x 3 Given the diagram below, find the dimensions of the rectangle if the area is 128 square feet. 4 The dimensions of a rectangle can be expressed as x + 3 and x 8. If the area of the rectangle is 60 square inches, what is the value of x? x 1 x The length of a rectangular garden is 4 meters more 6 than its width. The area of the rectangle is 60 meters. Find the dimensions of the rectangle. The length of a rectangle is 6 meters less than its width. Find the dimensions of the rectangle if its area is 27 square meters. Gina Wilson, 2013

50 PROJECTILE MOTION 1. A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation = + gives the height of the ball after seconds. a. Find the maximum height of the ball. 1a. b. b. How many seconds will it take for the ball to reach the ground? 2. An apple is launched directly upward at 64 feet per second from a platform 80 feet high. The equation for this apple s height at time seconds after launch is = a. b. a. Find the maximum height of the apple. b. How many seconds will it take for the apple to reach the ground? 3. In science class, the students were asked to create a container to hold an egg. They would then drop this container from a window 25 feet above the ground. The equation = +, gives the container s height after seconds. 3a. b. a. Find the maximum height of the container. b. How many seconds will it take for the container to reach the ground? Gina Wilson, 2013

51 4. A penny is dropped off the Empire State Building, which is 1,250 feet tall. If the penny s pathway can be modeled by the equation = +, how long would it take the penny to strike a 6 foot tall person? Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object s height at time seconds after launch is = +. How long will it take the fireworks to reach the ground? The Apollo s Chariot, a rollercoaster at Busch Gardens, moves at 110 feet per second. The equation of the ride can be represented by the equation = + +. What is the maximum height reached by this ride? Eva is jumping on a trampoline. Her height at time can be modeled by the equation = + +. Would Eva reach a height of 14 feet? An astronaut on the Moon throws a baseball upward with an initial velocity of 10 meters per second, letting go of the baseball 2 meters above the ground. The equation of the baseball pathway can be modeled by = The same experiment is done on Earth, in which the pathway is modeled by equation = How much longer would the ball stay in the air on the Moon compared to on Earth? 8. Gina Wilson, 2013

52 Name: Unit 8: Quadratic Equations Date: Bell: Homework 10: Quadratic Word Problems ** This is a 2-page document! ** Area Problems: 1. Given the diagram below find the value of x if the area is 21 square meters. x 2. The dimensions of a rectangle can be given by x + 7 and x + 2. If the area of the rectangle is 66 square inches, what are the dimensions of the rectangle? x 4 3. The length of a rectangle is 6 meters more than its width. If the area of the rectangle is 135 square meters, find its dimensions. 4. The length of a rectangle is 1 meter less than its width. The area of the rectangle is 42 square meters. Find the dimensions of the rectangle. Projectile Motion Problems: 5. When a cannonball is fired, the equation of its pathway can be modeled by h = -16t t. a. Find the maximum height of the cannonball. b. Find the time it will take for the cannonball to reach the ground. Gina Wilson, 2013

53 6. When Joey dives off a diving board, the equation of his pathway can be modeled by h = -16t t a. Find Joey s maximum height. b. Find the time it will take for Joey to reach the water. 7. A toy rocket is launched from a platform that is 48 feet high. The rocket s height above the ground is modeled by h = -16t t a. Find the maximum height of the rocket. b. Find the time it will take for the rocket to reach the ground. 8. At the end of the school year, Rachel and Amber go to the roof of a 12-story building and throw their Algebra book off the edge. The equation of the pathway that each girl s textbook takes is given below. By how many seconds does Rachel s textbook beat Amber s to the ground? Rachel: h = -16t t Amber: h = -16t t Gina Wilson, 2013

54 Linear Vs. Quadratic Models LINEAR QUADRATIC Equation: Equation: Directions: Use a graph to determine the model. Then, find the equation for the best fit. 1 2 x y x y Linear or Quadratic? Equation: 3 x y Linear or Quadratic? Equation: x y Linear or Quadratic? Equation: Linear or Quadratic? Equation: Gina Wilson, 2013

55 5 6 x y x y Linear or Quadratic? Equation: x y Linear or Quadratic? Equation: x y Linear or Quadratic? Linear or Quadratic? 9 Equation: The value, V, of a computer between 1999 and 2003 is given in the table. Equation: t V Linear or Quadratic? Equation: Value of the computer in 2008? 10 A coin is thrown off the top of the Statue of Liberty, which is 305 feet from the ground. The height, h, of the coin is recorded after each second, t, in the table below. t h Linear or Quadratic? Equation: Height of the coin after 7 sec? Gina Wilson, 2013

56 Name: Date: Bell: Unit 8: Quadratic Equations Homework 11: Linear and Quadratic Models ** This is a 2-page document! ** Determine if a linear or quadratic model exists. Then, find the equation for best fit x y x y Linear or Quadratic? Equation: x y Linear or Quadratic? Equation: x y Linear or Quadratic? Equation: Linear or Quadratic? Equation: 5. A real-estate agent is trying to determine the relationship between the distance a 3-bedroom home is from New York City and its average selling price. He records the data for 6 homes shown below. x y 755, , , , , ,000 *x = miles from NYC; y = cost of home Linear or Quadratic? Approximate cost of home 90 miles from NYC? Equation: Gina Wilson, 2013

57 6. A football is kicked into the air with an initial upward velocity of 82 feet per second. Its height, h (in feet), is recorded at various seconds, t, in the table below. t h Linear or Quadratic? Equation: Height of the football after 5 sec? 7. A frog is jumping onto a lilly pad. It s height, h (in feet), is recorded at various seconds, t, in the table below. t h Linear or Quadratic? Equation: Height of frog after 6 sec? 8. The table below shows the number of students enrolled at Mapleton High School since x y Linear or Quadratic? Equation: Number of students to enroll in 2011? Gina Wilson, 2013

58 Entrance Ticket Name: Determine if the following data represents a linear or quadratic model. Then, using the equation for the line or curve of best fit, solve for the missing value. 1) The local theater puts on an annual play. The table below shows the number of auditions for the lead role each year since Using an equation to model the data, approximate the number of auditions that will be held in Year Auditions ) A toy rocket was fired into the air. The height, h, of the rocket at time t seconds is recorded in the table below. Using an equation to model the data, find the height of the rocket after 5 seconds. t (sec) h (ft) Entrance Ticket Name: Determine if the following data represents a linear or quadratic model. Then, using the equation for the line or curve of best fit, solve for the missing value. 1) The local theater puts on an annual play. The table below shows the number of auditions for the lead role each year since Using an equation to model the data, approximate the number of auditions that will be held in Year Auditions ) A toy rocket was fired into the air. The height, h, of the rocket at time t seconds is recorded in the table below. Using an equation to model the data, find the height of the rocket after 5 seconds. t (sec) h (ft)

59 QUADRATIC INEQUALITIES Step 1: Find the and. Step 2: Use your calculator to generate a table of values. Step 3: Graph the parabola. *Use a line for < or > symbols. *Use a line for or symbols. Step 4: Use a to determine where to shade. EXAMPLES: 1. > x y x y 3. < x y x y Gina Wilson, 2013

60 5. < x y x y < x y x y < x y x y Gina Wilson, 2013

61 Name: Date: Bell: Unit 8: Quadratic Equations Homework 12: Quadratic Inequalities ** This is a 2-page document! ** Directions: Graph the following quadratic inequalities. Shade to show the possible solutions. 1. y > x 2 + 2x 3 2. y 2x 2 12x y < -x 2 + 8x y < x 2 4x y -2x x y 3x x + 25 Gina Wilson, 2013

62 7. y x 2 6x 8. y > -x 2 + 4x 7 9. y 2x 2 4x 10. y < -x Gina Wilson, 2013

63 Topic #1: Axis of Symmetry & Vertex 1. = Unit 8 Test Study Guide Quadratic Equations 2. = = 9 Axis of Symmetry Vertex Axis of Symmetry Vertex Axis of Symmetry Vertex Topic #2: Graphing Quadratic Equations 4. y = x 2 8x + 15 Axis of Symmetry: Vertex: Domain: Range: Zeros: 5. y = -x 2 + 4x 4 Axis of Symmetry: Vertex: Domain: Range: Zeros: 6. y = -2x 2 3 Axis of Symmetry: Vertex: Domain: Range: Zeros: Topic #3: Solving Quadratic Equations (By Factoring!) 7. 7 = = +2 Gina Wilson, 2013

64 = = = = = = = =24 Topic #4: Solving Quadratic Equations (By the Quadratic Formula!) 17. = = = =81 Gina Wilson, 2013

65 Topic #5: Area Problems 21. If the area of the rectangle below is 42 inches squared, find the value of x. x The length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions. x + 8 Topic #6: Projectile Motion 23. Natalie found a tennis ball outside a tennis court. She picked up the ball and threw it over the fence into the court. The path of the ball can be represented by h = -16t t + 5 a. Find the maximum height of the tennis ball. b. How long will it take to reach the ground? 24. A circus acrobat is shot out of a cannon with an initial upward speed of 50 ft/s. The equation for the acrobat s pathway can be modeled by h = -16t t + 4. a. Find the maximum height of the acrobat. b. How long will it take to reach the ground? Topic #7: Linear & Quadratic Modeling 25. Debbie recorded the time it took seven children of different ages to run a lap around the track. Using an equation to model the data, find the approximate time it would take for a 6 year old to run a lap. AGE (years) TIME (sec) A pistol is accidently discharged vertically in the air. The height, h, of the bullet at time t seconds is recorded in the table below. Using an equation to model the data, find the height of the pistol after 10 seconds. t (sec) h (ft) Gina Wilson, 2013

66 UNIT 8 TEST REVIEW Find Someone Who! Directions: Trade papers with 12 different people to solve the following problems. Find the axis of symmetry and vertex for the following quadratic equation: 1 2 Identify the factors of the quadratic equation below. Write your answers in the boxes. y = -x 2 + 8x 23 Axis of Symmetry Vertex Name: Name: 3 Write the quadratic equation below in standard form. y = (x 3) Solve by factoring: x 2 30 = 7x 5 Name: Solve by factoring: 6 Name: Solve by factoring: 3x 2 + 3x = 60 10x x = 2x + 6 s Name: Name: Gina Wilson, 2013

67 7 Solve by factoring: 8 Solve by factoring: 12x 2 20x = 0 2x 2 = x Name: Solve by factoring: (x + 9)(x 2) = Name: Which quadratic equation has roots of -5 and 2? A. y = x 2 + 3x 10 B. y = x 2 3x 10 C. y = x 2 + 7x + 10 D. y = x 2 7x + 10 Name: Name: The height of an arrow shot into the air can be represented by the equation h = -16t t + 6, where t is time in seconds and h is height in feet. 11 What is the maximum height of the arrow? 12 How long will it take the arrow to reach the ground? Name: Name: Gina Wilson, 2013

68 Name: Date: Bell: Algebra I Unit 8 Test (Quadratic Equations) SHOW ALL WORK NEEDED TO ANSWER EACH QUESTION! PLACE YOUR FINAL ANWER IN THE BOX. GOOD LUCK! 1. Find the axis of symmetry and vertex for the equation below. y = -x 2 4x Find the axis of symmetry and vertex for the equation below. y = 2x Axis of Symmetry Vertex Axis of Symmetry Vertex 3. Use the graph below to fill in the blanks. Axis of Symmetry: Vertex: Domain: Range: Zeros: Equation: A. y = x 2 + 2x + 3 C. y = -x 2 + 2x + 3 B. y = x 2 2x + 3 D. y = -x 2 2x Which graph represents the equation y = (x + 2)(x 4)? A. B. C. D. Gina Wilson, 2013

69 5. Choose two binomials that could represent the factors of the parabola shown in the graph. Write your answers in the boxes. x + 2 x 2 x + 7 x 7 y = ( )( ) 6. Select the equation(s) that could represent parabola graphed below. y = (x 5)(x + 1) y = x 2 4x 5 y = (x + 5)(x 1) y = (x + 2) 2 9 y = x 2 + 4x 5 y = (x 2) Which equation is equivalent to the equation below? y = (x 2) Find the solution(s) to the equation below. x x = 24 A. y = x 2 1 B. y = x C. y = x 2 4x 1 D. y = x 2 4x Find the solution(s) to the equation below. x x = 4x Find the solution(s) to the equation below. 4x 2 24 = 20x Gina Wilson, 2013

70 11. Find the solution(s) to the equation below. 5x x = x Find the solution(s) to the equation below. x 2 9x = Find the solution(s) to the equation below. 4x = Find the solution(s) to the equation below. (x 1)(x + 3) = Find the solution(s) to the equation below. (x 4) 2 = The profit equation for a manufacturing company is P = x , where P is profit, and x is number of units sold. For what number of units sold does the company break even? (P = 0) A. 50 units sold B. 100 units sold C. 500 units sold D units sold 17. Which equation has roots -2 and 3? 18. A. y = x 2 + x 6 B. y = x 2 x 6 C. y = x 2 + 5x + 6 D. y = x 2 5x + 6 Find the solution(s) to the equation below. x 2 + 7x 10 = 0 Gina Wilson, 2013

71 19. Find the solution(s) to the equation below. 3x 2 = x If the area of the rectangle below is 39 square feet, find the value of x. x 2 x Select the quadratic equation(s) that have two roots. y = x 2 8x 20 y = x y = x 2 2x + 1 y = x 2 25 y = 4x x April shoots an arrow upward at a speed of 80 feet per second from a platform 25 feet high. The pathway of the arrow can be represented by the equation h = -16t t + 25, where h is the height and t is the time in seconds. What is the maximum height of the arrow? A. 80 feet B. 90 feet C. 125 feet D. 140 feet 23. A rock is dropped from bridge 320 feet above a river. The pathway that the rock takes can be modeled by the equation h = -16t How long will it take the rock to reach the river? A. 2.5 sec B. 3.5 sec C. 3.8 sec D. 4.5 sec Gina Wilson, 2013

72 24. The table shows student enrollment at a college by year. Using an equation to model the data, find the approximate enrollment for the year x y A people B people C people D people 25. The Sears Tower, at 1,451 feet, is one of the tallest structures in the United States. A penny is thrown from the top of the tower. The height, h, of the penny is recorded after each second, t, in the table. Using an equation to model the data, find the approximate height of the penny after 7 seconds. t h A. 907 feet B. 912 feet C. 923 feet D. 928 feet Bonus: Find the solution(s) to the quadratic equation below. x ( x 8) 3( x+ 2) = 2( x+ 9) Gina Wilson, 2013

73 THANK YOU for purchasing this product! Please stop back at my store and let me know how it went! (By leaving feedback, you earn TpT Credits towards future purchases!) STAY CONNECTED! Blog: Pinterest: Facebook: CREDITS: Fonts provided by KevinandAmanda.com Frames provided by The Enlightened Elephant 2013 Gina Wilson, All Things Algebra Products by Gina Wilson (All Things Algebra) may be used by the purchaser for their classroom use only. All rights reserved. No part of this publication may be reproduced, distributed, or transmitted without the written permission of the author. This includes posting this product on the internet in any form, including classroom/personal websites or network drives. If you wish to share this product with your team or colleagues, you may purchase additional licenses from my store at a discounted price!

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92 Quadratic Equations in Vertex Form What is vertex form? y = a(x h) 2 + k where (h, k) is the vertex of the parabola. How do we convert this back to standard form standard form? Use!

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95 Name: Unit 8: Quadratic Equations Date: Bell: Homework 4: Solving Quadratics by Factoring (Day 1) ** This is a 2-page document! **

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102 Writing Quadratic Equations by Identifying the Roots! 1 y = ( )( ) x + 4 x y = x + 2x y = ( )( ) x - 7 x y = x - 15x y = ( )( ) x + 8 x y = x + 11x y = ( )( ) x + 1 x y = x - 4x - 5

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105 Name: Unit 8: Quadratic Equations Date: Bell: Homework 6: Solving Quadratics by The Quadratic Formula ** This is a 2-page document! **

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117 Name: Unit 8: Quadratic Equations Date: Bell: Homework 9: Solving Quadratics Review (All Methods) ** This is a 2-page document! **

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123 Name: Unit 8: Quadratic Equations Date: Bell: Homework 10: Quadratic Word Problems ** This is a 2-page document! **

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127 Name: Date: Bell: Unit 8: Quadratic Equations Homework 11: Linear and Quadratic Models ** This is a 2-page document! **

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How do you find the quadratic equation in projectile motion?

What is vertex form?

Which equations have no real solution?