Question 1170722
The highway mileage min miles per gallon for a compact car is approximated by m(s) = -0.025s^2+2.45s-30 where s is the speed in miles per hour.

a.If the car is traveling 65mph, what will the highway mileage be?
s = 65, therefore
m(s) = -0.025(65^2) + 2.45(65) - 30 
m(s) = -.025(4225) + 159.25 - 30
m(s) = -105.625 + 129.25
m(s) = 23.625 mpg
:
b.If the car is traveling 20mph, what will the highway mileage be?
s = 20
m(s) = -0.025(400)+2.45(20)-30 
m(s) = -10 + 49 - 30
m(s) = 9 mpg
:
c.What speed will the car be traveling if the mileage is 28 miles per gallon?
-0.025s^2 + 2.45s - 30 = 28
-0.025s^2 + 2.45s - 30 - 28 = 0
-0.025s^2 + 2.45s - 58 = 0 
use the quadratic formula a=-.025, b=2.45, c=-58
I got a positive solution of:
s = 40 mph
:
d. What speed will the car be traveling if the mileage is 0 miles per gallon?
-0.025s^2 + 2.45s - 30 = 0
using the quadratic formula; a=-.025, b=2.45, c=-30
Got a rather silly answer of 14.35 mph when mpg = 0
:
e.What is the maximum mileage for this compact car to the nearest tenth of a mile per gallon? What speed results in this mileage?
That will occur on the axis of symmetry, x=-b/(2a)
s = {{{(-2.45)/(2*-.025)}}}
s = 49 mph 
Find the mpg
m(s) = -0.025(49^2) + 2.45(49) - 30
m(s) =-.025(2401) + 120.05 - 30
M(s) = -60.025 + 90.05
m(s) = 30.025 ~ 30 mpg
:
Graphically
{{{ graph( 300, 200, -10, 100, -10, 50, -.025x^2+2.45x-30, 30, 24) }}}

vertical y is mpg, horizontal x is mph, green line is mpg=30, blueline is 24 mpg