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