Check It Out! Example 4 The highway mileage m in miles per gallon for a compact car is approximately by m(s) = –0.025s2 + 2.45s – 30, where s is the speed.

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Check It Out! Example 4 The highway mileage m in miles per gallon for a compact car is approximately by m(s) = –0.025s2 + 2.45s – 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?

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 - = - =

Check It Out! Example 4 Continued Step 2 Substitute this s-value into m to find the corresponding maximum, m(s). m(s) = –0.025s2 + 2.45s – 30 Substitute 49 for r. m(49) = –0.025(49)2 + 2.45(49) – 30 m(49) ≈ 30 Use a calculator. The maximum mileage is 30 mi/gal at 49 mi/h.

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.

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.

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.

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.

HW pg. 328 #’s 30 – 34, 47, 48