Answer
$ a.\quad G$ is even.
$ b.\quad$local maximum of $400$ at $x=-4$.
$ c.\quad A=1612.8$ sq.units
Work Step by Step
$a.$
$G(-x)=-(-x)^{4}+32(-x)^{2}+144=-x^{4}+32x+144=G(x)$
$G(-x)=G(x)$, so the function is even.
$b.$
Being even, its graph has y-axis symmetry.
If $(4,400)$ is a local maximum point, then the point symmetric to it,
$(-4,400)$ is on the graph and is also a local maximum point.
$c.$
Because of symmetry relative to the y-axis, the area enclosed
between $x=-6$ and the origin
equals the area enclosed from the origin to $x=6$
$A=1612.8$ sq.units