Math 154B Name_____ Solving Using the Quadratic Formula Worksheet The Quadratic Formula : For Quadratic equations : 02cbxax, aacbbx242 Solve each equation Using the Quadratic Formula . 1. 0201142xx 2. 02452xx 3. 332xx 4. xx552 5. 12xx 6. xx8142 7. 015742xx 8. 01032xx 9. 32xx 10. xx142322 11. 4822xx 12. xx183922 13. 01352xx 14. 1255052xx Answers: 1. 4,45xx 2. 3,8xx 3. 2213x 4. 255x 5. 251x 6. 252x 7. 3,45xx 8. 5,2xx 9. 2131x 10. 237x 11. 6,8xx 12. 239x 13. x = not a real number 14. 5x
Solving Using the Quadratic Formula Worksheet The Quadratic Formula: For quadratic equations: ax 2 bx c 0, a b b ac x 2 2 4 Solve each equation using the Quadratic Formula. 1. 4x 2 11x 20 0 2. x 2 5x 24 0 3. x2 3x 3 4. x2 5 5x 5. x2 x 1 6. 4x2 1 8x 7. 4x 2 7x 15 0 8. x 2 3x 10 0. 9.
1 Math 154B Name_____ Solving Using the Quadratic Formula Worksheet The Quadratic Formula : For Quadratic equations : 02cbxax, aacbbx242 Solve each equation Using the Quadratic Formula . 1. 0201142xx 2. 02452xx 3. 332xx 4. xx552 5. 12xx 6. xx8142 7. 015742xx 8.
01032xx 9. 32xx 10. xx142322 11. 4822xx 12. xx183922 13. 01352xx 14. 1255052xx Answers: 1. 4,45xx 2. 3,8xx 3. 2213x 4. 255x 5. 251x 6. 252x 7. 3,45xx 8. 5,2xx 9. 2131x 10. 237x 11. 6,8xx 12. 239x 13. x = not a real number 14. 5xTranscription of Math 154B Name Solving Using the Quadratic Formula ...
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Math 154BName_____________________Solving Using the Quadratic Formula WorksheetThe Quadratic Formula:For quadratic equations:02cbxaxaacbbx242Solve each equation using the Quadratic Formula.,
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9.32xx10.xx14232211.4822xx12.xx18392213.01352xx14.12550
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Math 154B Name_____________________ Solving Using the Quadratic Formula Worksheet
The Quadratic Formula: For quadratic equations: ax 2 bx c 0 ,
a
b b ac x 2
24Solve each equation using the Quadratic Formula. 1. 4 x 211 x 20 0 2. x 25 x 24 0
x 23 x 3
- x 255 x
x 2 x 1
- 4 x 218 x
4 x 27 x 15 0
Answers:
- , 4 4
x 5 x
x ,8 x 3
2
x 321
4.2x 55
5. 2x 15
6.2x 25
7. , 34x 5 x
x ,2 x 5
2
x 113
10.2x 73
11. x ,8 x 612.29 3x
- x = not a real number
- x 5
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Kuta Software - Infinite Algebra 2 Name___________________________________
Properties of Parabolas Date________________ Period____
Identify the vertex of each.
- y = x 2 + 16 x + 64 2) y = 2 x 2 − 4 x − 2
y = − x 2 + 18 x − 75 4) y = − x 2 + 12 x − 10
Graph each equation.
- y = x 2 − 2 x − 3
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
6)y = − x 2 − 6 x − 10
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
Identify the min/max value of each. Then sketch the graph.
- f ( x ) = − x 2 + 8 x − 20
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
- f ( x ) = −
x 2 +
43x −
163x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
-1-
©n P 2 h 0 S 1 e 2 e BKSu 9 tSaU XSuoHfCtAwea 4 rRe 2 9 LtLEC 1 .m p aAElOlm 6 rSiPgihLtisO uryefswePrYvQevdy r aMda 4 dlex Qw 5 iWt 3 hw nIdnkf 0 iZnsijtqez 5 AWldg 8 ewbgrVaL 52 E Worksheet by Kuta Software LLC
- f ( x ) = x 2 + 2 x − 1
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
- f ( x ) = − x 2 − 10 x − 30
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8
Identify the vertex, axis of symmetry, and min/max value of each.
f ( x ) = 3 x 2 − 54 x + 241 12) f ( x ) = x 2 − 18 x + 86
f ( x ) = −
x 2 +
485x −
1145f ( x ) = − x 2 − 20 x − 46
f ( x ) = −
x 2 + 7
f ( x ) = x 2 − 12 x + 44
f ( x ) =
x 2 − x + 9
- f ( x ) = x 2 + 4 x + 5
-2-
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- f ( x ) = x 2 + 2 x − 1
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8 Min value = −
- f ( x ) = − x 2 − 10 x − 30
x
y
−8 −6 −4 −2 2 4 6 8
−
−
−
−
2
4
6
8 Max value = −
Identify the vertex, axis of symmetry, and min/max value of each.
- f ( x ) = 3 x 2 − 54 x + 241
Vertex: ( 9 , −2)
Axis of Sym.: x = 9 Min value = −
- f ( x ) = x 2 − 18 x + 86
Vertex: ( 9 , 5 )
Axis of Sym.: x = 9 Min value = 5
- f ( x ) = −
x 2 +
485x −
1145Vertex: ( 6 , 6 )
Axis of Sym.: x = 6 Max value = 6
- f ( x ) = − x 2 − 20 x − 46
Vertex: (−5, 4 )
Axis of Sym.: x = − Max value = 4
- f ( x ) = −
x 2 + 7
Vertex: ( 0 , 7 )
Axis of Sym.: x = 0 Max value = 7
- f ( x ) = x 2 − 12 x + 44
Vertex: ( 6 , 8 )
Axis of Sym.: x = 6 Min value = 8
- f ( x ) =
x 2 − x + 9
Vertex: ( 2 , 8 )
Axis of Sym.: x = 2 Min value = 8
- f ( x ) = x 2 + 4 x + 5
Vertex: (−2, 1 )
Axis of Sym.: x = − Min value = 1
-2-
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware
Sketching Quadratic Equations
A sketch graph of a quadratic function should illustrate the following:
The general shape of the graph (i. whether there is a maximum or a minimum) with respect to the x- and y- axes.
The location of the y-intercept (mark on the coordinates)
The roots of the equation (label the location on the x-axis)
The location of the vertex (mark on the coordinates)
You DO NOT need to measure out an accurate scale on a sketch graph, as long as you have provided the information listed above.
Sketch graphs of the following quadratic equations, showing y-intercepts, roots, and the vertex.
a. y x 2 11 x 10 b. y x 2 12 x 32
c. y x 2 6 x 5 d. y x 2 8 x 15
e. y x 2 12 x f. y x 2 5 x
g. y x 2 10 x 21 h. y x 2 11 x 10
i. y 2 x 2 13 x 7 j. y 2 x 2 5 x 12
k. l. y x 2 4 x 4 y x 2 6 x 9
g. shape: x 2 y–intercept: (0, – 21) Roots: (3, 0) and (7, 0) Vertex: (5, 4)
h. shape: x 2 y–intercept: (0, – 10) Roots: (1, 0) and (10, 0) Vertex: (5, 20).
i. shape: x 2 y–intercept: (0, – 7) Roots: (– 7 ,0) and (0 ,0) Vertex at (– 3, – 28)
j. shape: x 2 y–intercept: (0, – 12) Roots at (– 4, 0) and (1, 0) Vertex at (– 1, – 15)
k. shape: x 2 y–intercept: (0, 4) double zero and Vertex at (2, 0)
l. shape: x 2 y–intercept: (0, – 9) double zero and Vertex at (3, 0)
0
5
10
-2 -1 0 1 2 3 4 5 6 7 8 9 10
y x
0
10
20
-5 0 5 10 15
x
y
0
5
10
15
20
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
x
y
-16-
-8-
04
8
12
-6 -4 -2 0 2 4
y x