Answer
$f(x)=-2x^2+2$
Work Step by Step
This question is asking us to design a parabola with two horizontal intercepts. Let's consider the vertex of the parabola is $(0,2)$.Then we can write the parabola in the vertex form: $$\begin{aligned}
f(x) &= a(x-h)^2+k\\
&=a(x-0)^2+2\\
&=ax^2+2.
\end{aligned}$$ Because we took the vertex above the $x$-axis, let's take $a<0$ so that the parabola opens downward and therefore intersects the $x$-axis twice. For example ley $a=-2$: $$\begin{aligned}
f(x) &= -2x^2+ 2.
\end{aligned}$$ See the graph.
