The stream of water from a fountain follows a parabolic path. the stream reaches a maximum height of 7 feet, represented by a vertex of (4,7)
, and lands 8 feet from the water jet, represented by (8,0)
. write a function in vertex form that models the path of the stream.

First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.

If we need the vertex to be at , the equation will contain a term.

If we start with we have a parabola, concave down, with vertex at and a maximum of 0.

So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be

We have

Now we only have to fix the fact that this parabola doesn't land at , because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want

such that:

Plugging these values gets us

As you can see in the attached figure, the parabola we get satisfies all the requests.

idk

step-by-step explanation: