Ans: A
A is true. Rewrite the equation of the graph to $y = -(x – 6)^2 + 16$.
A is true. Rewrite the equation of the graph to $y = -(x – 6)^2 + 16$.
By comparing to the form $y = a(x – h)^2 + k$, we know that the graph opens downwards and the maximum value of $y$ is $16$. Therefore, the graph cuts the $x$ axis.
B is not true. As mentioned above, the graph opens downwards.
C is not true. By expanding the equation of the graph, we have
$\begin{array}{rcl}
y & = & 16 – (x – 6)^2 \\
y & = & 16 – x^2 + 12x -36 \\
y & = & -x^2 + 12x – 20
\end{array}$
Therefore, the $y$-intercept is $-20$.
D is not true. Since the $y$-intercept of the graph is $-20$, then the graph does not pass through the origin.
