Answer
$25$ inches rainfall per year
$13.5$ inches of growth
Work Step by Step
The quadratic function
$$f(x)=-0.02x^2+x+1$$
has negative leading coefficient, therefore its graph is a parabola which opens downward and has a maximum in the vertex.
Bring the function to the vertex form $f(x)=a(x-h)^2+k$:
$$\begin{align*}
f(x)&=-0.02x^2+x+1\\
&=-0.02(x^2-50x+625)+13.5\\
&=-0.02(x-25)^2+13.5.
\end{align*}$$
Identify the constants $a$, $h$, $k$:
$$\begin{align*}
a&=-0.02\\
h&=25\\
k&=13.5.
\end{align*}$$
Determine the vertex of the function:
$$(h,k)=(25,13.5).$$
So the amount of rainfall per year that results in maximum tree growth is $25$ inches, while the maximum yearly growth is $13.5$ inches.
