Key Concepts
Exponential functionAn exponential function is the product of an initial amount and a constant ratio raised to a power. Show
 Transformations of exponential functionsVertical translation of graphsAlgebra: f(x) = ax+k Horizontal translation of graphsAlgebra: f(x) = a(x−h) PolynomialA polynomial expression is an expression that has constants and variables by means of addition, multiplication, and exponentiation to a non-negative integer power. Factorizing x2+bx+c = 0To the factor, a trinomial of the form x2+bx+c, find a factor pair of c that has a sum of b. Then use the factors you found to write the binomials that have a product equal to the trinomial. Quadratic functionA function f defined by f(x) = ax2+bx+c, where a, b and c are real numbers and a≠0a≠0, is called a quadratic function. Graph of a quadratic equationThe graph of a quadratic function is a curve called a parabola.
Quadratic parent functionThe quadratic parent function is f(x) = x2. It is the simplest function in the quadratic function family.
Graph of f(x) = ax2
Graph of f(x) = ax2 when a<0
Compare the rate of change in the graph
Exercise1. How does the value of a in g(x) = -4x2 affect the graph when compared to the graph of the quadratic parent function? 2. In which interval is the function increasing? 3. How does the value of a in h(x) = 0.15x2 affect the graph when compared to the graph of the quadratic parent function? 4. Write a quadratic equation for the area of the figure given. Find the area of the figure for the given value of x. x=5 Concept MapA function 𝑓 defined by 𝑓(𝑥) = 𝑎𝑥2 + 𝑏𝑥 + 𝑐, where 𝑎, 𝑏, and 𝑐 are real numbers and 𝑎 ≠ 0, is called a quadratic function. The graph of a quadratic function is a curve called a parabola. What we have learned
What are the different types of quadratic functions?1 Standard Form of Quadratic Function. The standard form of a quadratic function is f (x)=a (x-h) 2 +k, where (h,k) is the vertex of the parabola. 2 Domain and Range of Quadratic Function. ... 3 Graphing Quadratic Function. ... 4 Maxima and Minima of Quadratic Function. ... 5 Quadratic Functions Formula. ...
What are the characteristics of a quadratic function in vertex form?Identifying Characteristics of Quadratic Functions in Vertex Form: y = a (x-p)^2 + q y = a(x−p)2 +q y = 2 {left ({x - 3} right)^2} - 8 y =2(x−3)2 −8 is a quadratic function in vertex form.
What are the 8 characteristics of a quadratic formula?Eight Characteristics of Quadratic Formulas. The line of symmetry is always a vertical line of the form x = n, where n is a real number, and its axis of symmetry is the vertical line x =0. The x -intercepts are the points at which a parabola intersects the x -axis. These points are also known as zeroes, roots, solutions, and solution sets.
What is the standard form of a quadratic function?A quadratic function can be in different forms: standard form, vertex form, and intercept form. Here are the general forms of each of them: Standard form: f (x) = ax 2 + bx + c, where a ≠ 0. Vertex form: f (x) = a (x - h) 2 + k, where a ≠ 0 and (h, k) is the vertex of the parabola representing the quadratic function.
What characteristic of a quadratic function is found in its standard form?The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).
What are the characteristics of a quadratic graph?The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.
Which of the following is one of the characteristics of a quadratic equation?The different characteristics of quadratic functions that are most commonly analyzed are the vertex (the maximum or minimum point), the x-intercepts (the zeros), and the axis of symmetry.
What are the 3 forms of quadratic functions?There are three commonly-used forms of quadratics:. Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.. Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2). Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.. |
What are the characteristics of quadratic functions
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