Answer
The standard form of the given parabola is \[g\left( x \right)=-3{{\left( x+2 \right)}^{2}}+4\]
Work Step by Step
We know that a quadratic function can be expressed in the standard form as $f\left( x \right)=a{{\left( x-h \right)}^{2}}+k$ corresponding to which the graph is a parabola whose vertex is the point $\left( h,k \right)$. The parabola attains its maximum value at 4 so it must be opening downwards. Thus $a<0$; therefore, $f\left( h \right)=k$ is the maximum. Therefore, $k=4$.
The parabola attains its maximum at -2, Thus $h=-2$. Also, the parabola is downwards so the shape of the parabola is $g\left( x \right)=-3{{x}^{2}}$.
Now, substitute the obtained results in the standard form to get:
$\begin{align}
& g\left( x \right)=-3{{\left( x-\left( -2 \right) \right)}^{2}}+4 \\
& =-3{{\left( x+2 \right)}^{2}}+4
\end{align}$
Hence, the parabola is expressed in standard form as $g\left( x \right)=-3{{\left( x+2 \right)}^{2}}+4$.
