Answer
$f(x)=-2x^{2}-5$
Work Step by Step
The equation of the parabola will be in the form $f(x)=a(x-h)^{2}+k$
For $a\gt 0$, the minimum function value is $k$.
For $a\lt 0$, the maximum function value is $k.$
Here, the maximum is $(0,-5)$, which means $a$ is negative and $-5$ is the maximum function value.
Therefore the shape of the parabola is $f(x)=-2x^{2}$.
$f(x)=a(x-h)^{2}+k$
Substitute $a=-2,h=0,k=-5$
$f(x)=-2x^{2}-5$
