Question

please help, last question I will ask for today
The maximum gas mileage for a compact car is estimated using the graph shown below.


The average gas mileage for an SUV is modeled by the function m(s)=−0.015(s−55)2+15, where s is the SUV's speed in miles per hour.


The difference in maximum mileage between these two vehicles is _____ mpg (miles per gallon).


Enter the number that correctly fills in the blank in the previous sentence.

Answer 1

what's the maximum of the graph?

Answer 2

no idea

Answer 3

think of it visually, what's the highest point on the graph?

Answer 4

33

Answer 5

so the graph's maximum is at 33 mpg
for reference \(−0.015(x−55)^2+15\)?

Answer 6

\(-0.015(x-55)^2+15\)

Answer 7

so i just plug it in?

Answer 8

no that's a different equation, I'm just asking if it's right

Answer 9

oh yeah it is right

Answer 10

give me a bit, I can't remember how to find the max. I th ink we have to factor it

Answer 11

ok

Answer 12

let's set y to 0

Answer 13

\(y=-0.015(x-55)^2+15\)
\(0=-0.015(x-55)^2+15\) subtract 15
\(-15=-0.015(x-55)^2\) divide both sides by -0.015
\(1000=(x-55)^2\)

Answer 14

can you solve it now?

Answer 15

so now you just plug in or more steps

Answer 16

wolfram says the other maximum is at x=55

Answer 17

so the suv is 55 mpg and the compact is 33

Answer 18

wait no

Answer 19

we want the y value

Answer 20

don"t you have to subtract them because it says what is the difference wouldn"t it be 22

Answer 21

at x=55,

y=-0.015(55-55)^2+15
y=-0.015(0)+15
y=15

Answer 22

oh ok

Answer 23

apologies, it's been a while so I'm kinda winging it

Answer 24

its ok :)

Answer 25

anyhow, the compact has a max of 33mpg and the SUV 15mpg

Answer 26

so you would subtract the 33 and the 15 right?

Answer 27

probably

Answer 28

thanks.