Chapter 4: Quadratic Functions and Equations Section 4.1: Quadratic Functions and Transformation

Section 4.1: Quadratic Functions and Transformations Goal: To identify and graph quadratic functions

Section 4.1: Quadratic Functions and Transformations Quadratic Function: a function in the form of : f(x) = ax2 + bx + c, where a ≠ 0 Parabola: The graph of a quadratic function Vertex Form: f(x) = a(x – h)2 + k, where a ≠ 0 Vertex of the parabola is (h, k) Axis of Symmetry: a line that divides the parabola into two mirror images The axis is located at x = h

Section 4.1: Quadratic Functions and Transformations Parabola:

Section 4.1: Quadratic Functions and Transformations Examples: Compare the graphs of f(x) = and f(x) = 2x2 by using an x/y chart

Section 4.1: Quadratic Functions and Transformations Minimum Value: the y-coordinate of the vertex if a > 0 Maximum Value: the y-coordinate of the vertex if a < 0

Section 4.1: Quadratic Functions and Transformations You try: 1. Graph f (x) =

Section 4.1: Quadratic Functions and Transformations Translations:

Section 4.1: Quadratic Functions and Transformations You try: Graph each function. How is each graph a translation of f (x) = x2? a) g (x) = (x – 3)2 b) h (x) = x2 + 1

Section 4.1: Quadratic Functions and Transformations You try: 3. For y = ½ (x – 3)2 – 5, what are vertex, the axis of symmetry, the minimum or maximum value, the domain, and the range?

Section 4.1: Quadratic Functions and Transformations You try: 4. What is the graph of f (x) = -3 (x + 5)2 + 2?

Section 4.1: Quadratic Functions and Transformations You can use the vertex and a point on the parabola to write the equation of the parabola: In f (x) = a (x – h)2 + k, plug the vertex in for h and k and any point on the parabola for x and y to find the value of a then write the equation Example: Write an equation of a parabola if its vertex is (-1, 2) and the point (3, 4) is on the parabola

Section 4.1: Quadratic Functions and Transformations You try: 4. The arch of the Sidney Harbor Bridge is approximately 500 meters long and 85 meters high. What quadratic function models the curve of the arch? Assume the arch starts at (0, 0).

Section 4.1: Quadratic Functions and Transformations Homework: Pg. 199 #8-36 (even), # 44, 46, 49-51 (all)