Unit 7 Day 5

After today we will be able to: Describe the translations of a parabola. Write the equation of a quadratic given the vertex and a point on the parabola. Change the equation of a quadratic from standard to vertex form.

Vertex Form y = a(x – h) 2 + k Vertex → (h,k) Identify the vertex of the following quadratics: 1. y = (x – 2) 2 2. y = (x + 3) 2 – 1 3. y = -3(x + 2) y = 2(x + 3) 2 + 1

Translations of Quadratics The vertex form of a quadratic equation is a translation of the parent function y = x 2.

Translations of Quadratics Shifts: The vertex will shift to the ________ if h is negative The vertex will shift to the ________ if h is positive The vertex will shift to the ________ if k is positive The vertex will shift to the ________ if k is negative

Identifying the Translation Given the following functions, identify the vertex and the translation from y = x 2. 1.y = (x + 4) y = -(x – 3) y = ½ (x + 1) 2 4.y = 3(x – 2) 2 – 2 **The translations should match the vertex of the parabola.

Writing a Quadratic Equations Write the equation of a quadratic with a vertex of (-1,0) and the parabola goes through the point (-2,2). **Plug in the vertex and the point and solve for a

Try one! Write an equation of a parabola that has a vertex of (2,3) and goes through the point (4,1).

One More! Write an equation in vertex form: Vertex (1,2) and y – intercept of 6

Converting from Standard to Vertex form Things needed: Find Vertex using x = -b/2a, and y = f(-b/2a). This is your h and k. Then use the a from standard form. Standard: y = ax 2 + bx + c

Example Convert from standard form to vertex form. y = -3x x + 5

Example Convert from standard form to vertex form. y = x 2 + 2x + 5

Try Some! Convert each quadratic from standard to vertex form. 1.y = x 2 + 6x – 5 2.y = 3x 2 – 12x y = -2x 2 + 4x – 3