Function Inverse Help Please

Clovis is standing at the edge of a cliff, which slopes 6 feet downward from him for every 1 horizontal foot. He launches a small model rocket from where he is standing. With the origin of the coordinate system located where he is standing, and the x-axis extending horizontally, the path of the rocket is described by the formula y = −3x^2 + 120x.

(a) Give a function *h* = *f*(*x*)

relating the height *h* of the rocket above the sloping ground to its *x*-coordinate.

**-3x^2 + 126x**

(b) Find the maximum height of the rocket above the sloping ground. What is its *x*-coordinate when it is at its maximum height?

**1332, 121**

(c) Clovis measures its height *h* of the rocket above the sloping ground while it is going up. Give a function *x* = *g*(*h*)

relating the *x*-coordinate of the rocket to *h*.

How would I go about solving for c?

Re: Function Inverse Help Please

Hey VARSOFFON.

With regards to part c, you want to find the region where the rocket is increasing which means that this will be from where it time = 0 to the time of the maximum.

Hint: Consider completing the square and the take the right branch of the square root.

Re: Function Inverse Help Please

Ohh okay thank you very much!

Re: Function Inverse Help Please

I think you mean for part b) the *x*-coordinate at the maximum height is 21, with a height of 1323.

For part c), use:

$\displaystyle h(x)=-3x^2+126x$ where $\displaystyle 0\le x\le21$

Now write this is standard quadratic form:

$\displaystyle 3x^2-126x+h=0$

Use the quadratic formula, and take the root in the closed interval [0,21].