Bell Ringer 1. What is the Quadratic Formula? 2. How do you determine the Discriminant? 3. Which form of a Quadratic Function gives you the y-intercept immediately? 4. Which transformations are rigid motions? 5. Which transformation changes the size of a graph?

Transformations of the Quadratic Parent Function f(x) = x2 Tuesday March 10, 2015

Each function has a “parent”. I call it the “OG” (original graph). Parent Function Each function has a “parent”. I call it the “OG” (original graph). The Quadratic OG is f(x) = x2

Transformations of f(x) = x2 Transformations include: 1. Horizontal translation 2. Vertical translation 3. Reflection 4. Dilations

Horizontal Translations Vertex form: f(x) = a (x-h)2 + k (aka Complete the Square form) If h is positive, the quadratic is translated right that amount. If h is negative, the quadratic is translated left that amount. REMEMBER>>> it’s the opposite EX: (x – 5) h is positive 5

Vertical Translations: Vertex form: f(x) = a (x-h)2 + k (aka Complete the Square form) If k is positive, the quadratic is translated up that amount. If k is negative, the quadratic is translated down that amount.

Reflection & Dilations Vertex form: f(x) = a (x-h)2 + k (aka Complete the Square form) If a is negative, the quadratic flips across the x-axis. If a is a fraction, the quadratic has a vertical compression (opens wider). If a is greater than 1, the quadratic has a vertical stretch (opens skinnier).

1. Convert the quadratic to vertex form (complete the square). So, how do I tell (without graphing) what happens to a quadratic in standard form? 1. Convert the quadratic to vertex form (complete the square). 2. Look at “h”, “k”, and “a” to see what happens to the “OG”.

Assignments Classwork: Parabola Worksheet (graphing, focus and directrix) Homework: Transformations of the Quadratic Parent Function, f(x)=x2 Remember… Tomorrow Study Guide Thursday, Test Unit 3. Don’t miss it!