6.6 Analyzing Graphs of Quadratic Functions

Write a Quadratic Equation in Vertex form

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.

abx2

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)

abx2

cabb

abay

22

2

Find the vertex of the Quadratic Equation

974)1(2

71412

144

224

742

2

2

yy

y

x

xxy

Find the vertex of the Quadratic Equation

91

9,1

khVertex

The Vertex form of the Quadratic Equation

91

9,1

742 2

khVertex

xxy khxay 2

?aisWhat

The Vertex form of the Quadratic Equation

91

9,1

742 2

khVertex

xxy khxay 2

?aisWhat

2a

The Vertex form of the Quadratic Equation

91

9,1

742 2

khVertex

xxy khxay 2

2a

912

912

2

2

xy

xy

Write the Quadratic Equation in Vertex form

Find a, h and ka= 1h = -1k = 3

khxay 2

3421

4121

1122

42

2

2

yyy

x

xxy

Write the Quadratic Equation in Vertex form

Find a, h and k

a= 1h = -1k = 3

khxay 2

31

31

2

2

xy

xy

422 xxy

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

Let see what changes happen when you change “a”

Let see what changes happen when you change “a”

Let see what changes happen when you change “a”

The larger the “a”, the skinner the graphWhat if “a” is a fraction?

Let see what changes happen when you change “a”

What if “a” is a fraction?

What if we change “h” in the Vertex

Let a = 1, k = 0

Changing the “h” moves the graph Left or Right.

What if we change “k” in the Vertex

Let a = 1, h = 0

“k” moves the graph up or down.

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

2)1( 2

2

xay

khxay

Write an equation

Given vertex (1, 2) and point on the graph passing through (3, 4)

x=3, y=4

2)1( 2

2

xay

khxay

2)13(4 2 aSolve for “a”

Write an equation

a = ½

2)1( 2

2

xay

khxay

Solve for “a”

a

aaa

a

4242

244224

2)13(4

2

2

Write an equation

a = ½

2)1( 2

2

xay

khxay

Final Answer

a

aaa

a

4242

244224

2)13(42

2

2121 2 xy

Homework

Page 326 – 327 # 15 – 25 odd,

27, 31, 39 – 45 odd

Homework

Page 326 – 327 #16 – 26 even,

28, 32, 40 – 46 even