Answer:
42.25 feet
Step-by-step explanation:
The maximum of a quadratic can be found by finding the vertex of the parabola that the quadratic creates visually on a graph.
So first step to find the maximum height is to find the x-coordinate of the vertex.
After you find the x-coordinate of the vertex, you will want to find the y that corresponds by using the given equation,
. The y-coordinate we will get will be the maximum height.
Let's start.
The x-coordinate of the vertex is
.
compare to
.
We have that
.
Let's plug into
with those values.
with ![a=-16,b=52,c=0](https://tex.z-dn.net/?f=a%3D-16%2Cb%3D52%2Cc%3D0)
.
The vertex's x-coordinate is 13/8.
Now to find the corresponding y-coordinate.
![y=52(\frac{13}{8})-16(\frac{13}{8})^2](https://tex.z-dn.net/?f=y%3D52%28%5Cfrac%7B13%7D%7B8%7D%29-16%28%5Cfrac%7B13%7D%7B8%7D%29%5E2)
I'm going to just put this in the calculator:
![y=\frac{169}{4} \text{ or } 42.25](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B169%7D%7B4%7D%20%5Ctext%7B%20or%20%7D%2042.25)
So the maximum is 42.25 feet.