1. Quadratics Day 2! VERTEX FORM Unit 6 Quadratic Functions Math II

2. VERTEX FORM ! y = a (x – h ) 2 + k -Where a is the same a from Standard Form -The Vertex of the quadratic is at ( h, k ) -We can easily graph a quadratic when it is in vertex form

3. Converting from Vertex to Standard Form Example: y = -2(x – 4) 2 + 5 = -2(x 2 – 8x + 16) + 5 = -2x 2 + 16x – 32 + 5 = -2x 2 + 16x – 27 Vertex Form: Square the binomial Distribute the coefficient of the trinomial…. Combine “like” terms Standard Form!

4. Example: Convert each quadratic to Standard Form. 1.y = 5(x + 2) 2 – 9 1.y = -3(x – 4) 2 + 7 1.(x – 2) 2 + 6

5. Review Example: Find the Axis of Symmetry of Vertex. 1.y = -2x 2 + 4x – 9 a = ____, b = ____, c = ____ 1.y = x 2 – 10 a = ____, b = ____, c = ____ 1.y = x 2 + 4x – 1 a = ____, b = ____, c = ____ 1.y = -2x 2 + 8x – 8 a = ____, b = ____, c = ____

6. Converting Standard Form to Vertex Form Step 1 : Determine the a value from standard form Step 2 : Find the vertex. – Use x = -b/2a to find the x coordinate – Substitute x in for the original equation to find y Step 3 : Substitute vertex and a to vertex form.

7. Example: Convert the quadratic to Vertex Form. a = 8  b = -16, c = 27 Vertex: (x-coordinate) (y-coordinate) Vertex : (1, 19) Vertex Form: y = 8(x – 1) 2 + 19 y = 8x 2 – 16x + 27

8. Example: Convert the quadratic to Vertex Form. y = 5x 2 – 40x + 67

9. Your turn!: Convert the quadratic to Vertex Form. 1.y = x 2 – 9 1.y = 7x 2 + 28x + 19 1.y = -2x 2 – 24x – 75

10. Writing the equation of a Quadratic given the vertex and a point.. Example: Find the equation of the quadratic with vertex (0, 0) and passes through the point (-2, 8) y = a (x – 0) 2 + 0 Substitute vertex in for h and k 8 = a (-2 – 0) 2 + 0Substitute x and y values in 8 = a (-2) 2 Simplify and solve for a 8 = 4 a 2 = a Vertex Form: y = 2(x – 0) 2 + 0 OR y = 2x 2

11. Example: Find each quadratic function with the given vertex that passes through the given point. Write in Standard Form. 1.Vertex (2, 0) passing through (1, 3) 1.Vertex (-3, 0) passing through (-5, -4) 1.Vertex (2, 5) passing through (3, 7) 1.Vertex (-3, 4) passing through (0, 0)