Question

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?

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=49Put value of h to get Kk=-0.025(49)^2+2.45×(49)-30k=  -30.025k=  -30.0