Which of the following equations determines a parabola which opens downward and has a vertex at \((-5, 9)\)?

(A) \(\ \ y=-(x-5)^{2}-5\)

(B) \(\ \ y=-(x-9)^{2}-5\)

(C) \(\ \ y=-(x+5)^{2}+9\)

(D) \(\ \ y=(x+5)^{2}+9\)

(E) \(\ \ y=(x-5)^{2}+9\)

If \(x>-9\), which of the following is equivalent to \(\sqrt{x+81}=x+9\)?

(A) \(\ \ x=x-72\) for \(x>-9\)

(B) \(\ \ x=x-9\) for \(x>-9\)

(C) \(\ \ x=x+9\) for \(x>-9\)

(D) \(\ \ x=x^{2}+18x\) for \(x>-9\)

(E) \(\ \ x=x^{2}+18x+81\) for \(x>-9\)

\[(6x+6)(6-x)=0\]

What are all the possible values of \(x\)?

\(\begin{align}
&\text{(A)}\ \ -1\\

&\text{(B)}\ \ -1\ \text{and}\ 6\\

&\text{(C)}\ \ 0\\

&\text{(D)}\ \ 0\ \text{and}\ 6\\

&\text{(E)}\ \ 0, 1\ \text{and}\ 6\\

\end{align}\)

If \((x-5)^{2}=225\) and \(x<0\), which of the following equals \(x\)?

(A) \(\ \ -230\)

(B) \(\ \ -20\)

(C) \(\ \ -10\)

(D) \(\ \ -15\)

(E) \(\ \ 20\)

(A) It will be wider.

(B) It will be narrower.

(C) It will move \(4\) units to the left.

(D) It will move \(4\) units to the right.

(E) It will move \(4\) units downward.

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