Question 1

Given the quadratic function $$f(x) = -5(x - 3)^2$ + 12$$, 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 $$(x - 3)^2$ is negative.

Question 2

For the function $$f(x) = -5(x - 3)^2$ + 12$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, 12)$$

Question 3

What is the axis of symmetry for the function $$f(x) = -5(x - 3)^2$ + 12$$?

Accepted Answer

$$x = 3$$

Question 4

What is the maximum value of the function $$f(x) = -5(x - 3)^2$ + 12$$?

Accepted Answer

$$12$$

Question 5

Which of the following best describes the range of the function $$f(x) = -5(x - 3)^2$ + 12$$?

Accepted Answer

$$(-\infty, 12]$$

Question 6

Suppose $$f(x) = -5(x - 3)^2$ + 12$$ models the height (in meters) of a ball thrown upward, where $$x is $$time in seconds. What is the maximum height the ball reaches?

Accepted Answer

$$12$$ meters

Question 7

For the function $$f(x) = -5(x - 3)^2$ + 12$$, what is the $$y-$$intercept?

Accepted Answer

$$f(0) = -5(0 - 3)^2$ + 12 = -5(9) + 12 = -45 + 12 = -33$$

Question 8

Which of the following is the standard form of the function $$f(x) = -5(x - 3)^2$ + 12$$?

Accepted Answer

$$f(x) = -5x^2$ + 30x - 33$$

Question 9

If $$f(x) = -5(x - 3)^2$ + 12$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

Question 10

Which of the following statements is TRUE about the domain of $$f(x) = -5(x - 3)^2$ + 12$$?

Accepted Answer

The domain is all real numbers.

Question 11

If $$f(x) = -5(x - 3)^2$ + 12$$, what is the value of $$x$$ for which $$f(x) = 7$$?

Accepted Answer

$$x = 3 \pm 1$$

Question 12

Which of the following best describes the vertex of the function $$f(x) = -5(x - 3)^2$ + 12$$?

Accepted Answer

It is the maximum point of the graph.

Question 13

If $$f(x) = -5(x - 3)^2$ + 12$$, what is the effect of the $$-5$$ coefficient on the graph?

Accepted Answer

It makes the parabola open downward and narrower.

Question 14

Suppose $$f(x) = -5(x - 3)^2$ + 12$$ models the profit (in thousands of dollars) for producing $$x$$ units. What is the maximum profit, and at how many units is it achieved?

Accepted Answer

Maximum profit is $$12$$ thousand dollars at $$x = 3$$ units.

Question 15

Which transformation occurs to the parent function $$y = x^2$ to obtain f(x) = -5(x$$ - $$3)^2 + 12$?

Accepted Answer

Shift right 3 units, reflect over $$x-$$axis, vertically stretch by 5, shift up 12 units.

Quadratic Functions and Their Properties: Study Notes

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