Question 1

Given the quadratic function $$f(x) = -2(x-3)^2$ + 8$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, 8)$$

Question 2

For the quadratic function $$f(x) = ax^2$ + bx + c$$, if $$a \u003e 0$$, which of the following is true?

Accepted Answer

The parabola opens upward and the vertex is a minimum point.

Question 3

What is the axis of symmetry for the quadratic function $$g(x) = a(x-h)^2$ + k$$?

Accepted Answer

$$x = h$$

Question 4

A football is punted and its height is modeled by $$f(x) = -0.1x^2$ + 1.18x + 2. At $$what horizontal distance does the football reach its maximum height?

Accepted Answer

$$x = 59$$ feet

Question 5

Given $$f(x) = (x+3)^2$ + 1$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 10)$$

Question 6

For the quadratic $$f(x) = -x^2$ - 2x + 1$$, what is the range of the function?

Accepted Answer

$$(-\infty, 2]$$

Question 7

If the vertex of $$f(x) = a(x-h)^2$ + k is at$$ $$(h, k)$$ and $$k \u003c 0$$, what transformation has occurred compared to $$f(x) = ax^2$?

Accepted Answer

The graph has shifted down $$|k|$$ units.

Question 8

A rectangular field is to be fenced with 100 yards of fencing. What is the maximum area that can be enclosed?

Accepted Answer

$$625$$ square yards

Question 9

Which formula gives the $$x-$$coordinate of the vertex for $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$x = -\frac{b}{2a}$$

Question 10

If $$f(x) = -3x^2$ + 6x - 13$$, what is the maximum value of the function?

Accepted Answer

$$-10$$

Question 11

For the quadratic $$f(x) = -2(x-3)^2$ + 8$$, what are the $$x-$$intercepts?

Accepted Answer

$$(1, 0)$$ and $$(5, 0)$$

Question 12

Which of the following best describes the domain of any quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 13

If $$f(x) = -0.1x^2$ + 1.18x + 2$$ models the height of a football, how far does the football travel before hitting the ground?

Accepted Answer

$$119.7$$ feet

Question 14

Given $$f(x) = -x^2$ - 2x + 1$$, use the quadratic formula to find one of the $$x-$$intercepts.

Accepted Answer

$$x \approx 0.4$$

Question 15

If $$f(x) = a(x-h)^2$ + k$$ and $$a \u003c 0$$, which statement is true?

Accepted Answer

The parabola opens downward and the vertex is a maximum.

Question 16

A blocker stands 6 feet from the punter. According to $$f(x) = -0.1x^2$ + 1.18x + 2$$, how high must the blocker reach to block the punt?

Accepted Answer

$$8.72$$ feet

Question 17

If $$f(x) = (x+3)^2$ + 1$$, what are the $$x-$$intercepts?

Accepted Answer

There are no real $$x-$$intercepts.

Question 18

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Quadratic Functions and Their Properties

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