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Functions

Concept Quizzes

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) $$\ \ 20$$

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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