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 $(4,-6)$. Start with the vertex form of a parabola and set $h= 4$ and $k= -6$. $$\begin{aligned}
f(x) &= a(x-h)^2+ k=a(x-4)^2-6.
\end{aligned}$$ Since the parabola opens upward, the value of the constant $ a$ must be positive. For $a= 4$, we have: $$\begin{aligned}
y &= 4(x-4)^2 -6.
\end{aligned}$$
A) The graph has two horizontal intercepts.
B) It has one vertical intercept.
