SAT Question 91e7ea5e: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. It's given that the graph of $y=h(x)$ intersects the $x$-axis at $(0,0)$ and $(t,0)$, where $t$ is a constant. Since this graph intersects the $x$-axis when $y=0$ or when $h(x)=0$, it follows that $h(0)=0$ and $h(t)=0$. If $h(t)=0$, then $0=2(t-4{)}^2-32$. Adding $32$ to both sides of this equation yields $32=2(t-4{)}^2$. Dividing both sides of this equation by $2$ yields $16=(t-4{)}^2$. Taking the square root of both sides of this equation yields $4=t-4$. Adding $4$ to both sides of this equation yields $8=t$. Therefore, the value of $t$ is $8$.