Math CentralQuandaries & Queries


Question from rachelle, a student:

under certain condition, it is found that the cost of operating an automobile as a
function of speed is approximated by a quadratic equation. use the data shown
below to find the function. then use the function to determine the cost of operating
the automobile at 60mph.

(in miles per hour)
operating cost
per mile(in cents)
10 22
20 20
50 20


Hi Rachelle,

Suppose the speed is x miles per hour and the operating cost is y cents per mile. If the operating cost is a quadratic function of the speed then

y = ax2 + bx + c for some numbers a, b and c.

Hence when the speed is 10 mph and the cost is 22 cents per mile

102 a + 10 b + c = 22.

Use the second and third rows of data to produce two more equations in a, b and c. Solve these three equations for a, b and c. Write the resulting quadratic equation and substitute x = 60 mph to find the operating cost at that speed.


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