Quadratic Functions: f(x) = a(x – h)2

Table of Contents 46: Warm-Up 47: How Do I Graph an Equation in the Form a(x – h)2?

Warm-Up Explain how the graph f(x) = x2 will be transformed for each of the following. 1. P(x) = -x2 + 50 2. C(x) = -3x2 3. K(x) = ½x2 – 16

Pop Quiz Each of the following parabolas represents a quadratic function for the form f(x) = ax2 + c. For each parabola, circle whether the values for “a” and “c” are positive, negative, or zero.

Learning Intention/Success Criteria LI: We are learning how to graph parabolic functions in the form a(x – h)2 SC: I know how to -recognize if a quadratic function opens upwards or downwards -graph parabolic functions -use a table of values to graph a function -find the y-intercept -

EQ: How Do I Graph an Equation in the Form a(x – h)2? 5/22/2019

Vertex The point where the parabola makes its sharpest turn Maximum Vertex The highest point in a parabola Only true when A is negative Minimum Vertex The lowest point in a parabola Only true when A is positive

Roots The solution to an equation in the form f(x) = 0. Where the line crosses the x-axis Called zeroes or x-intercepts

Example 1: Create a table and graph the function, as compared to the parent function f(x) = (x – 1)2 x Work f(x) -2 (-2 – 1)2 = (-3)2 9 -1 (-1 – 1)2 = (-2)2 4 (0 – 1)2 = (-1)2 1 1 (1 – 1)2 = (0)2 2 (2 – 1)2 = (1)2 1 3 (3 – 1)2 = (2)2 4 4 (4 – 1)2 = (3)2 9

x f(x) -2 9 -1 4 1 2 3 Vertex: (1, 0) x = 1 Axis of Symmetry:

Example 2: Create a table and graph the function, as compared to the parent function f(x) = (x + 2)2 x Work f(x) -5 (-5 + 2)2 = (-3)2 9 -4 (-4 +2)2 = (-2)2 4 -3 (-3 + 2)2 = (-1)2 1 -2 (-2 + 2)2 = (0)2 -1 (-1 + 2)2 = (1)2 1 (0 + 2)2 = (2)2 4 1 (1 + 2)2 = (3)2 9

x f(x) -5 9 -4 4 -3 1 -2 -1 Vertex: (-2, 0) x = -2 Axis of Symmetry:

Example 3: Create a table and graph the function, as compared to the parent function f(x) = 2(x – 1)2 x Work f(x) -2 2(-2 – 1)2 = 2(-3)2 18 -1 2(-1 – 1)2 = 2(-2)2 8 2(0 – 1)2 = 2(-1)2 2 1 2(1 – 1)2 = 2(0)2 2 2(2 – 1)2 = 2(1)2 2 3 2(3 – 1)2 = 2(2)2 8 4 2(4 – 1)2 = 2(3)2 18

x f(x) -2 18 -1 8 2 1 3 4 Vertex: (1, 0) x = 1 Axis of Symmetry:

Example 4: Create a table and graph the function, as compared to the parent function f(x) = -½(x + 2)2 x Work f(x) -8 -½(-8 + 2)2 = -½(-6)2 -18 -6 -½(-6 + 2)2 = -½(-4)2 -8 -4 -½(-4 + 2)2 = -½(-2)2 -2 -2 -½(-2 + 2)2 = -½(0)2 -½(0 + 2)2 = -½(2)2 -2 2 -½(2 + 2)2 = -½(4)2 -8 4 -½(4 + 2)2 = -½(6)2 -18

x f(x) -8 -18 -6 -4 -2 2 4 Vertex: (-2, 0) x = -2 Axis of Symmetry: