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Holt Algebra Properties of Quadratic Functions in Standard Form 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? Check It Out! Example 4

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Holt Algebra Properties of Quadratic Functions in Standard Form 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 = Check It Out! Example 4 Continued b s a

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

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Holt Algebra Properties of Quadratic Functions in Standard Form 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. Check It Out! Example 4 Continued

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Holt Algebra Properties of Quadratic Functions in Standard Form 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. Example 4: Area Application

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Holt Algebra Properties of Quadratic Functions in Standard Form 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. Example 4 Continued

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Holt Algebra Properties of Quadratic Functions in Standard Form Step 2 Substitute this x-value into A(x) to find the corresponding maximum, A(x). The maximum area of the garden is 75 sq. ft. A(x) = -3x x A(5) = -3(5) (5) A(5) = 75 Example 4 Continued Substitute 5 for x. Use a calculator.

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Holt Algebra Properties of Quadratic Functions in Standard Form HW pg. 328 #’s 30 – 34, 47, 48

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