Question 1

Given the quadratic function $f(x) = -\left(x - 3\right)^2 + 12$, which of the following statements is TRUE about the direction in which the parabola opens?

Accepted Answer

The parabola opens downward because the coefficient of the squared term is negative.

Question 2

For the function $f(x) = -\left(x - 3\right)^2 + 12$, what are the coordinates of the vertex?

Accepted Answer

$(3, 12)$

Question 3

What is the axis of symmetry for the function $f(x) = -\left(x - 3\right)^2 + 12$?

Accepted Answer

$x = 3$

Question 4

What is the maximum value of the function $f(x) = -\left(x - 3\right)^2 + 12$?

Accepted Answer

$12$

Question 5

Which of the following best describes the range of the function $f(x) = -\left(x - 3\right)^2 + 12$?

Accepted Answer

$(-\infty, 12]$

Question 6

What is the $y$-intercept of the function $f(x) = -\left(x - 3\right)^2 + 12$?

Accepted Answer

$(0, 3)$

Question 7

Which of the following is the standard form of the function $f(x) = -\left(x - 3\right)^2 + 12$?

Accepted Answer

$f(x) = -x^2 + 6x + 3$

Question 8

If $f(x) = -\left(x - 3\right)^2 + 12$, for which value of $x$ does $f(x) = 0$?

Accepted Answer

$x = 3 \pm \sqrt{12}$

Question 9

Which of the following best describes the domain of $f(x) = -\left(x - 3\right)^2 + 12$?

Accepted Answer

$(-\infty, \infty)$

Question 10

Suppose the function $f(x) = -\left(x - 3\right)^2 + 12$ models the height (in meters) of a ball thrown upward, where $x$ is the time in seconds. What is the maximum height the ball reaches?

Accepted Answer

$12$ meters

Question 11

If $f(x) = -\left(x - 3\right)^2 + 12$, what is the value of $x$ when $f(x) = 8$?

Accepted Answer

$x = 3 \pm 2$

Question 12

Which of the following statements is TRUE about the symmetry of the graph of $f(x) = -\left(x - 3\right)^2 + 12$?

Accepted Answer

The graph is symmetric about the line $x = 3$.

Question 13

If the function $f(x) = -\left(x - 3\right)^2 + 12$ represents the profit (in dollars) from selling $x$ units, what is the maximum profit possible?

Accepted Answer

$12$ dollars

Question 14

Which of the following describes the effect of changing the $+12$ in $f(x) = -\left(x - 3\right)^2 + 12$ to $+8$?

Accepted Answer

The vertex moves down by 4 units.

Question 15

If $f(x) = -\left(x - 3\right)^2 + 12$, what is the interval of $x$ for which $f(x) \geq 8$?

Accepted Answer

$1 \leq x \leq 5$

Quadratic Functions: Graphs, Vertices, and Properties

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