1. ( ) EXAMPLE 6 Write a quadratic function in vertex form
Write y = x2 – 10x + 22 in vertex form. Then identify the vertex.
y = x2 – 10x + 22
Write original function.
y + ? = (x2 –10x + ? ) + 22
Prepare to complete the square.
Add
–10 2 ( ) =
(–5) 25
to each side.
y + 25 = (x2 – 10x + 25) + 22
y + 25 = (x – 5)2 + 22
Write x2 – 10x + 25 as a binomial squared.
y = (x – 5)2 – 3
Solve for y.
The vertex form of the function is y = (x – 5)2 – 3. The vertex is (5, – 3).
ANSWER

2. EXAMPLE 7
Find the maximum value of a quadratic function
Baseball
The height y (in feet) of a baseball t seconds after it is hit is given by this function:
y = –16t2 + 96t + 3
Find the maximum height of the baseball.
SOLUTION
The maximum height of the baseball is the y-coordinate of the vertex of the parabola with the given equation.

3. Find the maximum value of a quadratic function
EXAMPLE 7
Find the maximum value of a quadratic function
y = – 16t2 + 96t +3
Write original function.
y = – 16(t2 – 6t) +3
Factor –16 from first two terms.
y +(–16)(?) = –16(t2 –6t + ? ) + 3
Prepare to complete the square.
y +(–16)(9) = –16(t2 –6t + 9 ) + 3
Add
to each side.
(–16)(9)
y – 144 = –16(t – 3)2 + 3
Write t2 – 6t + 9 as a binomial squared.
y = –16(t – 3)
Solve for y.
The vertex is (3, 147), so the maximum height of the baseball is 147 feet.
ANSWER

4. ( ) GUIDED PRACTICE for Examples 6 and 7 13.
Write y = x2 – 8x + 17 in vertex form. Then identify the vertex.
y = x2 – 8x + 17
Write original function.
y + ? = (x2 –8x + ? ) + 17
Prepare to complete the square.
Add –8 2 ( ) =
(–4) 16
to each side.
y + 16 = (x2 – 8x + 16) + 17
Write x2 – 8x + 16 as a binomial squared.
y + 16 = (x – 4)2 + 17
y = (x – 4)2 + 1
Solve for y.
The vertex form of the function is y = (x – 4) The vertex is (4, 1).
ANSWER

5. ( ) GUIDED PRACTICE for Examples 6 and 7 14.
Write y = x2 + 6x + 3 in vertex form. Then identify the vertex.
y = x2 + 6x + 3
Write original function.
y + ? = (x2 + 6x + ? ) + 3
Prepare to complete the square.
Add 6 2 ( ) =
(3) 9
to each side.
y + 9 = (x2 + 6x + 9) + 3
Write x2 + 6x + 9 as a binomial squared.
y + 9 = (x + 3)2 + 3
y = (x + 3)2 – 6
Solve for y.
The vertex form of the function is y = (x + 3)2 – 6. The vertex is (– 3, – 6).
ANSWER

6. ( ) GUIDED PRACTICE for Examples 6 and 7 15.
Write f(x) = x2 – 4x – 4 in vertex form. Then identify the vertex.
f(x) = x2 – 4x – 4
Write original function.
y + ? = (x2 – 4x + ? ) – 4
Prepare to complete the square.
Add
– 4 2 ( ) =
(– 2) 4
to each side.
y + 4 = (x2 – 4x + 4) – 4
y + 4 = (x – 2)2 – 4
Write x2 – 4x + 4 as a binomial squared.
y = (x – 2)2 – 8
Solve for y.
The vertex form of the function is y = (x – 2)2 – 8. The vertex is (2 , – 8).
ANSWER

7. GUIDED PRACTICE for Examples 6 and 7 16.
What if ? In example 7, suppose the height of the baseball is given by y = – 16t2 + 80t + 2. Find the maximum height of the baseball.
SOLUTION
The maximum height of the baseball is the y-coordinate of the vertex of the parabola with the given equation.
y = – 16t2 + 80t +2
Write original function.
y = – 4((2t)2 – 20t) +2
Factor – 4 from first two terms.
y +(– 4)(?) = – 4((2t)2 – 20t + ? ) + 2
Prepare to complete the square.

8. GUIDED PRACTICE for Examples 6 and 7
y +(– 4)(25) = – 4((2t)2– 20t + 25 ) + 2
Add
to each side.
(–4)(25)
Write 2t2 – as a binomial squared.
y – 100 = – 4(2t – 5)2 + 2
y = – 4(2t – 5)
Solve for y.
The vertex is (5, 102), so the maximum height of the baseball is 102 feet.
ANSWER