1. Check It Out! Example 4
The highway mileage m in miles per gallon for a compact car is approximately by
m(s) = –0.025s s – 30, where s is the speed in miles per hour. What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? What speed results in this mileage?

2. Check It Out! Example 4 Continued
The maximum value will be at the vertex (s, m(s)).
Step 1 Find the s-value of the vertex using a = –0.025 and b = 2.45. ( )
2.45
0.02 2 5 49 b s a -
= - =

3. Check It Out! Example 4 Continued
Step 2 Substitute this s-value into m to find the corresponding maximum, m(s).
m(s) = –0.025s s – 30
Substitute 49 for r.
m(49) = –0.025(49) (49) – 30
m(49) ≈ 30
Use a calculator.
The maximum mileage is 30 mi/gal at 49 mi/h.

4. Check It Out! Example 4 Continued
Check Graph the function on a graphing calculator. Use the MAXIMUM feature under the CALCULATE menu to approximate the MAXIMUM. The graph supports the answer.

5. Example 4: Area Application
The area of a rectangular garden is modeled by A(x) = 3x(10 – x) where x is measured in feet. Determine the meaningful domain and range of the function and the maximum area of the garden.

6. The maximum value will be at the vertex (x, A(x)).
Example 4 Continued
The maximum value will be at the vertex (x, A(x)).
Step 1 Find the x-value of the vertex using a = -3 and b = 30.

7. The maximum area of the garden is 75 sq. ft.
Example 4 Continued
Step 2 Substitute this x-value into A(x) to find the corresponding maximum, A(x).
A(x) = -3x2 + 30x
Substitute 5 for x.
A(5) = -3(5)2 + 30(5)
A(5) = 75
Use a calculator.
The maximum area of the garden is 75 sq. ft.

8. HW pg. 328 #’s 30 – 34, 47, 48