SATMathematics Practice Test 1

Since g is an even function, $\mathit{g}\left(-4\right)=\mathit{g}\left(4\right)=8$.
Alternatively: First find the value of a, and then find $\mathit{g}\left(-4\right)$. Since $\mathit{g}\left(4\right)=8$,substituting 4 for x and 8 for g(x) gives $8=\mathit{a}{\left(4\right)}^2+=16\mathit{a}+$.
Solving this last equation gives $\mathit{a}=-1$.
Thus $\mathit{g}\left(\mathit{x}\right)=-{\mathit{x}}^2+24$ ,from which if follows that $\mathit{g}\left(-4\right)=-{\left(-4\right)}^2+24;\mathit{g}\left(-4\right)=-16+24;$ and $\mathit{g}\left(-4\right)=8$
Choices B, C, and D are incorrect because g is a function and there can only be one value of $\mathit{g}\left(-4\right).$