Answer
A) Two horizontal intercepts
B) One vertical intercept
Work Step by Step
This question is asking us to design a parabola with vertex at $(2,4)$. Start with the vertex form of a parabola and set $h= 2$ and $k= 4$.$$\begin{aligned}
f(x) &= a(x-h)^2+ k=a(x-2)^2+4.
\end{aligned}$$ Since the parabola opens downward, the value of the constant $ a$ must be negative. For $a= -2$, we have.
$$\begin{aligned}
y &= -2(x-2)^2+ 4.
\end{aligned}$$ A) The graph has two horizontal intercepts.
B) It has one vertical intercept.
