Vertex Form Of A Quadratic
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1The Vertex Form of a Quadratic Function
The vertex form of a quadratic function is:
2
y = a(x – h)
+ k
0011 0010 1010 1101 0001 0100 1 011
The vertex is read from the equation as (h, k).
Writing Quadratic Functions in
2
y = 3(x – 6)
– 8 has a vertex at ______________.
Vertex Form
Quadratic functions in standard form can be written in
2
2
1
1
b
−
vertex form by finding the vertex using x =
0011 0010 1010 1101 0001 0100 1011
2
a
Tuesday – 1/11/11
4
4
5
5
Section 3-5, Page 305
Converting to Vertex Form
Examples
b
−
Find the vertex of each quadratic function then write it
2
1. Use x =
to find the x-coordinate
Write y = -x
– 6x + 23 in
2
a
vertex form.
in vertex form.
of the vertex.
0011 0010 1010 1101 0001 0100 1 011
0011 0010 1010 1101 0001 0100 1 011
−
6
2
2
y = x
– 4x + 11
y = 2x
+ 10x – 3
=
−
=
−
x
3
−
( 2
) 1
2. Plug the x value (-3) into the original
function for x to find the rest of the
vertex.
2
2
2
1
1
y = -(-3)
– 6(-3) + 23
(-3, 32)
3. Write the vertex:
= -9 + 18 + 23 = 32
4. Use the vertex (-3, 32) and value of a
from the original function (-1) to
4
4
2
y = a(x – h)
+ k
write the function in vertex form.
5
5
y = -1(x + 3)
2
+ 32
Using a Graph to Write a Quadratic
The graph of a quadratic function can be used to write the equation in
Assignment
vertex form by using the vertex and a point on the graph.
0011 0010 1010 1101 0001 0100 1 011
0011 0010 1010 1101 0001 0100 1 011
Write an equation in vertex form of the function shown in the graph.
Pg. 309: 14 – 19 and 35 – 42
1. Find the vertex:
(3, 2)
2. Plug the vertex values into the vertex form
2
for a quadratic function: y = a(x – h)
+ k
2
2
1
1
2
y = a(x – 3)
+ 2
nd
3. Use a 2
point on the graph (-1, -2) to solve
4
4
for a by substituting the values in for x and y.
5
5
-2 = a(-1 – 3)
2
+ 2
-2 = a(16) + 2
The equation, in vertex
-4 = 16a
2
form, is: y = -¼(x – 3)
+ 2
-¼ = a
1
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