Answer
The vertex must be on the $x$-axis
Work Step by Step
This question is asking us to design a parabola with one horizontal intercept. Start with the vertex form of a parabola and set $h= 2$ and $k= 0$. $$\begin{aligned}
f(x) &= a(x-h)^2+ k=a(x-2)^2+0=a(x-2)^2.
\end{aligned}$$ Since the parabola opens downward, the value of the constant $ a$ must be negative. For $a= -2$, we have. $$\begin{aligned}
y &= -2(x-2)^2.
\end{aligned}$$ The vertex must be on the $x$-axis.
