Do Now 3/18/19

Punchline worksheet 14.2

Essential Question What are some characteristics of the graph of a quadratic function of the form f(x) = ax2? With your partner, complete Exploration 1 on pages 245-246 in your Student Journal

Chapter 8 “Graphing Quadratic Functions” (8.1) Graphing f(x) = ax² (8.2) Graphing f(x) = ax² + c (8.3) Graphing f(x) = ax² + bx + c (8.4) Graphing f(x) = a(x - h)² + k (8.5) Using Intercept Form (8.6) Comparing Linear, Exponential, and Quadratic Functions

Learning Goal Learning Target SWBAT graph quadratic functions SWBAT graph functions of the form f(x) = ax² and f(x) = ax² + c

Section 8.1 “Graphing f(x) = ax²” Quadratic Function A nonlinear function that can be written in the standard form f(x) = ax² + bx + c where a = 0. The graph of a quadratic function is in the form of a U-shape and called a parabola.

Graphing: f(x) = ax² y-axis f(x) = x² x-axis Vertex- Axis of Symmetry- “Parent Quadratic Function” x y 1 1 2 4 3 9 -1 1 -2 4 x-axis -3 9 Vertex- the lowest or highest point of the parabola Axis of Symmetry- the line that divides a parabola into 2 symmetric parts

Identifying Characteristics of Quadratic Functions Vertex: (-1, -2) Axis of Symmetry: x = -1 Domain: All real numbers Range: y ≥ -2

Identify the Characteristics of Quadratic Functions On Your Own Identify the Characteristics of Quadratic Functions

Graphing: y = ax² y = 3x² x-axis y-axis x y 1 3 2 12 -1 3 -2 12 “Parent Quadratic Function” y = x² x y 1 3 2 12 -1 3 -2 12 How does y = 3x² differ from the parent function y = x²? x-axis y-axis

Graphing: y = ax² y = -1/4x² x-axis y-axis x y 1 -1/4 2 -1 4 -4 6 -9 “Parent Quadratic Function” y = x² y = -1/4x² x y x-axis 1 -1/4 2 -1 4 -4 6 -9 -1 -1/4 -2 -1 -4 -4 y-axis -6 -9 y = -1/4x²

Graph the Following Functions On Your Own Graph the Following Functions g(x) = 5x2 g(x) = -3x2 g(x) = 1/3x2

Section 8.2 “Graphing f(x) = ax² + c”

Graphing: y = ax² + c x-axis y-axis “Parent Quadratic Function” f(x) = x² g(x) = 3x² -3 Compare to the graph of the parent function f(x) = x2 g(x) = 3x²– 3 x y -3 1 2 9 x-axis -1 -2 9 g(x) is a vertical translation down 3 units and a vertical stretch by a factor of 3 y-axis

Graph the Following Functions. Compare to the graph of f(x) = x2. On Your Own Graph the Following Functions. Compare to the graph of f(x) = x2. g(x) = x2 – 5 h(x) = x2 + 3

Zeros of a Function an x-value for which f(x) = 0. A zero of a function is an x-intercept of the graph of the function. To find the zeros of a function, graph the function and locate the x-intercepts. f(x) = -12x2 + 3 x = ½ and -½

Find the Zeros of the Functions On Your Own Find the Zeros of the Functions y = x2 – 1 f(x) = -x2 + 25 f(x) = 4x2 – 16 x = 1 & -1 x = 5 & -5 x = 2 & -2

Homework

Punchline worksheet 14.1