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

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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 \(x>-9\)

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

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}\)

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

(A) \(\ \ -230\)

(B) \(\ \ -20\)

(C) \(\ \ -10\)

(D) \(\ \ -15\)

(E) \(\ \ 20\)

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The parabola above has an equation \(y=n(x-4)^{2}-4\), where \(n\) is a positive constant. Which of the following best describes the graph of \(y=\frac{n}{4}(x-4)^{2}-4\) when compared to the graph above?

(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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