# Warm Up Honors Algebra 2 10/17/19 For each Warm Up Honors Algebra 2 10/17/19 For each translation of the point (2, 5), give the coordinates of the translated point. 1. 6 units down 2. 3 units right (2, 1)

(1, 5) For each function, evaluate f(-2), f(0), and f(3) 3. 4. 6; 6; 21 19; 1; 4 Objectives

Transform quadratic functions. Describe the effects of changes in the coefficients of y = a(x h)2 + k. Vocabulary quadratic function parabola vertex of a parabola vertex form

You studied linear functions of the form f(x) = mx + b. A quadratic function is a function that can be written in the form of f(x) = a (x h)2 + k (a 0). In a quadratic function, the variable is always squared. The table shows the linear and quadratic parent functions. Notice that the graph of the parent function f(x) = x2 is a U-shaped curve called a parabola. As with other functions, you can graph a quadratic function by plotting points with coordinates that make the equation true. You can also graph quadratic functions by

applying transformations to the parent function f(x) = x2. Transforming quadratic functions is similar to transforming linear functions. Example 1: Translating Quadratic Functions Use the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g(x) = (x 2)2 + 4

Identify h and k. g(x) = (x 2)2 + 4 h k Because h = 2, the graph is translated 2 units right. Because k = 4, the graph is translated 4 units up. Therefore, g is f translated 2 units right and 4 units up. Example 1B: Translating Quadratic Functions

Use the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g(x) = (x + 2)2 3 Identify h and k. g(x) = (x (2))2 + (3) h k

Because h = 2, the graph is translated 2 units left. Because k = 3, the graph is translated 3 units down. Therefore, g is f translated 2 units left and 4 units down. Check It Out! Example 1a Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g(x) = x2 5 Identify h and k.

g(x) = x2 5 k Because h = 0, the graph is not translated horizontally. Because k = 5, the graph is translated 5 units down. Therefore, g is f is translated 5 units down. Check It Out! Example 1b Use the graph of f(x) =x2 as a guide, describe the transformations and then graph each function.

g(x) = (x + 3)2 2 Identify h and k. g(x) = (x (3)) 2 + (2) h k Because h = 3, the graph is translated 3 units left. Because k = 2, the graph is translated 2 units down. Therefore, g is f translated 3 units left and 2 units down.

Recall that functions can also be reflected, stretched, or compressed. Example 2A: Reflecting, Stretching, and Compressing Quadratic Functions Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g (x )

=- 1 x 2 4 Because a is negative, g is a reflection of f

across the x-axis. Because |a| = , g is a vertical compression of f by a factor of . Example 2B: Reflecting, Stretching, and Compressing Quadratic Functions

Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g(x) =(3x)2 Because b = , g is a horizontal compression of f by a factor of .