1. 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!

2. 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

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)

4. 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
Put the vertex in the middle

5. 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?

6. 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! 

7. 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 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

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