SAT Question c946d5bd: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. Substituting $b$ for $x$ in the given equation yields $g(b+28)=\frac{1}{10}(b-a{)}^2(b-b{)}^2(b-c)$, which is equivalent to $g(b+28)=\frac{1}{10}(b-a{)}^2(0{)}^2(b-c)$, or $g(b+28)=0$. It follows that when $x=b+28$, $g(x)=0$. There are three points where the graph of $y=g(x)$ intersects the x-axis: $(-2,0)$, $(1,0)$, and $(3,0)$. Therefore, $g(-2)=0$, $g(1)=0$, and $g(3)=0$. It follows that either $b+28=-2$, $b+28=1$, or $b+28=3$. Subtracting $28$ from each side of the equation $b+28=-2$ yields $b=-30$. Subtracting $28$ from each side of the equation $b+28=1$ yields $b=-27$. Subtracting $28$ from each side of the equation $b+28=3$ yields $b=-25$. Thus, the value of $b$ must be either $-30$, $-27$, or $-25$. Of these values, only $-25$ is given as a choice.