Question 1

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

Accepted Answer

$$(3, 5)$$

Question 2

For the quadratic function $$f(x) = -x^2$ + 6x - 8$$, what is the axis of symmetry?

Accepted Answer

$$x = 3$$

Question 3

A company models its profit with the function $$P(x) = -2x^2$ + 16x + 5$$, where $$x is $$the number of units produced (in thousands). What is the maximum profit, and for how many units is it achieved?

Accepted Answer

Maximum profit is $$69$$ thousand dollars at $$x = 4$$ thousand units.

Question 4

Which of the following statements is TRUE about the graph of $$f(x) = a(x-h)^2$ + k$$ when $$a \u003c 0$$?

Accepted Answer

The parabola opens downward and the vertex is a maximum point.

Question 5

Find the range of the function $$f(x) = -3(x+2)^2$ + 7.$$

Accepted Answer

$$(-\infty, 7]$$

Question 6

A rectangular garden is to be built next to a wall, using 40 meters of fencing for the other three sides. What is the maximum area that can be enclosed?

Accepted Answer

$$133.33$$ square meters

Question 7

Given $$f(x) = x^2$ - 8x + 15$$, what is the minimum value of the function?

Accepted Answer

$$-1$$

Question 8

If the vertex of a parabola is at $$(2, -5)$$ and the parabola opens upward, which could be its equation?

Accepted Answer

$$f(x) = a(x-2)^2$ - 5$$, \ a \u003e 0$

Question 9

Which of the following best describes the effect of increasing $$k in$$ $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

The graph shifts upward by $$k$$ units.

Question 10

A projectile is launched from the ground and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t. $$What is the maximum height reached by the projectile?

Accepted Answer

$$20$$ meters

Question 11

Given $$f(x) = 4x^2$ - 12x + 7$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 1.5$$

Question 12

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

Accepted Answer

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

Question 13

If $$f(x) = (x+1)^2$ - 9$$, for which value of $$x$$ does $$f(x)$$ attain its minimum value?

Accepted Answer

$$x = -1$$

Question 14

A rectangular koi pond is to be built next to a wall using 24 feet of fencing for the other three sides. What should the width be to maximize the area?

Accepted Answer

$$6$$ feet

Question 15

For the function $$f(x) = -2(x-1)^2$ + 3$$, what is the range?

Accepted Answer

$$(-\infty, 3]$$

Question 16

Which transformation occurs when $$f(x) = (x-2)^2$ is changed to g(x$$) = $$(x-2)^2 + 5$?

Accepted Answer

The graph shifts up by $$5$$ units.

Question 17

Given $$f(x) = -x^2$ + 14x - 47$$, on which interval is the function increasing?

Accepted Answer

$$(-\infty, 7)$$

Question 18

If $$f(x) = x^2$ + 10x + 23$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-2$$

Question 19

Which of the following real-world scenarios can be modeled by a quadratic function?

Accepted Answer

The height of a ball thrown upward as a function of time.

Quadratic Functions: Graphs, Vertices, and Applications

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