HELP please!!!! A projectile is fired from the origin over horizontal
ground. Its altitude (in feet) is a function of its horizontal
distance (in feet) and is given by
y= 64x - 2x^2

a. Find the inverse function where the function is
increasing.
b. Use the inverse function to compute the horizontal
distance when the altitude of the projectile is
(i) 32 feet, (ii) 256 feet, and (iii) 512 feet.

Question

HELP please!!!! A projectile is fired from the origin over horizontal
ground. Its altitude (in feet) is a function of its horizontal
distance (in feet) and is given by 
y= 64x - 2x^2

a. Find the inverse function where the function is
increasing.
b. Use the inverse function to compute the horizontal
distance when the altitude of the projectile is 
(i) 32 feet, (ii) 256 feet, and (iii) 512 feet.

anonymous · Answer

For this problem divide out "-2" from your original equation then complete the square of the right side with the equal value on the left side to get$$y -512 = -2(x^2-32x + 256)$$ which simplifies to:$$y-512 = -2(x-16)^2$$ you then solve for "x" to find the horizontal distance the projectile is fired to given its respective height. This is part A.

For part B, you just plug in the given height for "y" to get the distance it travels for "x".
You can check if your answers are right by drawing a picture for each height it goes to and how far it traveled. It should look something similar to this:
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