1. 6.6 Analyzing Graphs of Quadratic Functions
Write a Quadratic Equation in Vertex form

2. Vertex form of the Quadratic Equation
So far the only way we seen the Quadratic Equation is ax2 + bx + c =0.
This form works great for the Quadratic Equation.
Vertex form works best for Graphing.
We need to remember how to find the vertex. The x part of the vertex come from part of the quadratic equation.

3. Vertex form of the Quadratic Equation
The x part of the vertex come from part of the quadratic equation.
To find the y part, we put the x part of the vertex.
The vertex as not (x, y), but (h, k)

4. Find the vertex of the Quadratic Equation

5. Find the vertex of the Quadratic Equation

6. The Vertex form of the Quadratic Equation

7. The Vertex form of the Quadratic Equation

8. The Vertex form of the Quadratic Equation

9. Write the Quadratic Equation in Vertex form
Find a, h and k
a= 1
h = -1
k = 3

10. Write the Quadratic Equation in Vertex form
Find a, h and k
a= 1
h = -1
k = 3

11. Vertex is better to use in graphing
y = 2(x - 3)2 – 2 Vertex (3 , -2)
Put in 4 for x, y = 2(3 - 4)2 – 2 (4, 0)
Then (2, 0)
is also a point

12. Let see what changes happen when you change “a”

13. Let see what changes happen when you change “a”

14. Let see what changes happen when you change “a”
The larger the “a”, the skinner the graph
What if “a” is a fraction?

15. Let see what changes happen when you change “a”
What if “a” is a fraction?

16. What if we change “h” in the Vertex
Let a = 1, k = 0
Changing the “h” moves the graph Left or Right.

17. What if we change “k” in the Vertex
Let a = 1, h = 0
“k” moves the graph up or down.

18. Write an equation Given the vertex and a point on the graph.
The vertex gives you “h” and “k”. We have to solve for “a”
Given vertex (1, 2) and point on the graph passing through (3, 4)
h =1; k = 2

19. Write an equation
Given vertex (1, 2) and point on the graph passing through (3, 4)
x=3, y=4
Solve for “a”

20. Write an equation
a = ½
Solve for “a”

21. Write an equation
a = ½
Final Answer

22. Homework
Page 326 – 327
# 15 – 25 odd,
27, 31,
39 – 45 odd

23. Homework
Page 326 – 327
# 16 – 26 even,
28, 32,
40 – 46 even