Graphing from Vertex Form Honors Algebra II with

Graphing from Vertex Form Honors Algebra II with Trigonometry Mrs. Stacey

Essential Stuff Essential Question • How do you write a quadratic function in vertex form? • How do you graph absolute value functions? Essential Vocabulary • Vertex • Translation

Parent Functions • The parent function is the most basic function of a group of functions. – Examples: y = x 2 y=|x| • When we graph, we are actually shifting and stretching the parent function. • We will look at two parent functions today – Quadratics and Absolute Value

Vertex Form of Quadratics • Quadratic functions can also be written in vertex form: y = a (x – h) 2 + k • In this form, the vertex is given as (h, k)

Translating Functions Each piece of the function changes the parent function in some way. y=a (x - h)² + k Multiply y-coordinates by a Shift up/down Follows the sign. Shift left/right Opposite of the sign.

Absolute Value Functions • Recall that the parent function is the original and the “easiest” of a group of functions. • The parent function for absolute value is y = |x|. • Let’s look at the graph of the parent function.

Graphs of Absolute Values Move k units up or down (same sign) Multiply y-coordinates by a Move h units left or right (opposite sign)

Graphing Quadratics and Absolute Values We can use the parent function to graph quadratics given in vertex form… 1. Identify the vertex 2. Multiply y-coordinates of points on parent function by the value of a 3. Shift all points h units horizontally (opposite sign) and all points k units

Homework: • Homework 4. 3: Graphing from Vertex Form