The highway mileage m in miles per gallon for a compact car is approximated 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?

Question

Miriam Lutz

Mathematics

11 November, 04:27

The highway mileage m in miles per gallon for a compact car is approximated 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?

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Christina Love · Answer 1

Highest mileage

m (s) = - 0.025s2 + 2.45s - 30

This quadratic equation lokks like a upside down parabolla

So as it is a form of mileage gunction of speed, its maximum value should be K

The "a" in the vertex form " y = a (x - h) 2 + k " of the quadratic is the same as the "a" in the common form of the quadratic equation, " y = ax2 + bx + c ".

To find the vertex, I look at the coefficients a, b, and c. The formula for the vertex gives me: Y = - 0.025s2 + 2.45s - 30

h = - b / 2a = - 2.45/2 * - 0.025=49 Put value of h to get K k=-0.025 (49) ^2+2.45 * (49) - 30 k = - 30.025 k = - 30.0