y = (-4/9x^2) + (24/9x) + 12

y = (-4/9(0)^2) + (24/9(0)) + 12

y = 0 + 0 + 12

y = 12

b. Get the derivative of y and solve for x to find out how far the ball has traveled when it reaches the maximum height

y’ = -8/9x + 24/9 = 0

-8/9x = -24/9

-8x = -24

x = -24/-8

x = 3

Now plug x into the original formula to find the maximum height:

y = (-4/9x^2) + (24/9x) + 12

y = (-4/9(3)^2) + (24/9(3)) + 12

y = (-4/9(9)) + (24/9(3)) + 12

y = (-4) + (8) + 12

y = 16

c. We can find the length of the punt by finding when the height is 0

(-4/9x^2) + (24/9x) + 12 = 0

4x^2 – 24x – 108 = 0

(4x – 36)(x + 3)

x + 3 = 0

x = -3

And

4x – 36 = 0

4x = 36

x = 36/4

x = 9

So the punt was 9 feet since -3 is not accepted

Sounds like one of my punts

I hope this helped

Kia