February 15, 2012 At the end of today, you will be able to use vertex form to find the vertex. Warm-up: Solve: 4x2 – 12x – 63 = 0 Solve by graphing:

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February 15, 2012 At the end of today, you will be able to use vertex form to find the vertex. Warm-up: Solve: 4x2 – 12x – 63 = 0 Solve by graphing: x2 – 4x – 12 < 0 HW 6.6: Pg. 326 #15-25odd + sketch graph! TEST next FRIDAY!

Lesson 6.6 Analyzing Quadratic Functions Transformations What direction does y = (x – 2)2 move? What direction does y = x2 – 3 move? y = x2 Right 2 Down 3

So what would y = (x – 2)2 – 3 look like? Right 2 and down 3 Where is the vertex? What is the axis of symmetry? x = 2 What is the vertex and axis of symmetry for y = (x + 4)2 – 5? (2, 3)

Vertex Form makes graphing Quadratics a little easier Vertex Form makes graphing Quadratics a little easier. y = a(x – h)2 + k The vertex will always be (h, k). You don’t need to use the formula x = -b/(2a) Example 1: Graph y = 2(x + 3)2 – 2 Vertex (-3, -2) Find more points, using your calculator or make a table: x y -2 0 -3 -2 Put the vertex in the middle -4 0

Individual Practice using Vertex Form y = a(x – h) + k Identify the Vertex, Axis of Symmetry, and sketch the graph. Graph y = (x – 5)2 – 3 Graph y = -2x2 + 5 *How can you tell if the parabola opens up or down without graphing it?

What if it’s not in VERTEX FORM!!! A perfect square trinomial is a trinomial ax2 + bx + c where c = (b/2)2 Let’s find c to make it a perfect square trinomial! 1. y = x2 + 16x + y = (x + 8)2 64 y = (x + 10)2 2. y = x2 + 20x + 100 y = (x – 9)2 3. y = x2 - 18x + 81 y = (x – 1)2 4. y = x2 - 2x + 1 This is called completing the square! 

Let’s put it all together Let’s put it all together! Write in Vertex Form and identify the vertex and axis of symmetry Example: y = x2 + 8x – 5 1. Use the first two terms to complete the square. y = x2 + 8x + - 5 16 - 16 y = (x + 4)2 − 21 2. Add and subtract the square to the equation (to keep the equation balanced). Vertex: (-4, 21) Axis of sym: x = -4 3. Write the perfect square trinomial and rewrite the equation in Vertex Form

Rewrite in Vertex Form, then identify the vertex and axis of symmetry. y = x2 + 6x + 2 y = x2 + 6x – 5 y = -2x2 + 8x – 3