Question 1

Which of the following is the correct vertex form of a quadratic function?

Accepted Answer

$$f(x) = a(x - h)^2$ + k$$

Question 2

Given the quadratic function $$f(x) = -2x^2$ + 4x - 1$$, what are the coordinates of its vertex?

Accepted Answer

$$(1, 1)$$

Question 3

A toy rocket is launched from a 1-meter tall platform with an initial velocity of $$44.1$$ meters per second. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 44.1t + 1. $$How long after launch does the rocket reach its maximum height?

Accepted Answer

$$t = 4.5$$ seconds

Question 4

What is the maximum height reached by the toy rocket described by $$h(t) = -4.9t^2$ + 44.1t + 1$$?

Accepted Answer

$$99.225$$ meters

Question 5

Which value must be added to $$x^2$$ + \frac{5}{6}x$$ to complete the square?

Accepted Answer

$$\frac{25}{144}$$

Question 6

Given the quadratic function $$f(x) = 2x^2$ - 4x - 3$$, what is its vertex in $$(h, k)$$ form?

Accepted Answer

$$(1, -5)$$

Question 7

For the quadratic function $$f(x) = ax^2$ + bx + c$$, which value of $$a$$ causes the graph to open downward?

Accepted Answer

$$a \u003c 0$$

Question 8

A rectangular pen is to be built using 100 ft of fencing, with one side along a river requiring no fencing. Mark wants to divide the pen into two equal sections with a partition perpendicular to the river. What is the length of the center partition that yields the maximum area?

Accepted Answer

$$33.33 ft$$

Question 9

Given the demand equation $$p = -\frac{1}{50}x + 10$$, where $$p is $$price and $$x is $$number of pairs of shoes sold, how many pairs should be sold to maximize revenue?

Accepted Answer

$$250$$ pairs

Question 10

Given the quadratic function $$f(x) = 2x^2$ - 6x + 1$$, does the function have a maximum or minimum value?

Accepted Answer

Minimum

Question 11

What is the axis of symmetry for the quadratic function $$f(x) = -2x^2$ - 4x + 5$$?

Accepted Answer

$$x = -2$$

Question 12

Which of the following is NOT a polynomial function?

Accepted Answer

$$g(x) = 4x^7$ - 3x^3$ + x^2$ + \frac{7}{x} - 3$$

Question 13

The vertex of a parabola given by $$f(x) = ax^2$ + bx + c is $$located at:

Accepted Answer

$$\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$$

Question 14

A country club has 400 members paying $$500 per month. For each 1 $$decrease in monthly dues, 2 additional members join. What monthly dues maximize revenue?

Accepted Answer

$$300$$

Question 15

Given the quadratic equation $$2x^2 + 2x - 3 = 0$, what are its solutions using the quadratic formula?

Accepted Answer

$$x = \frac{-1 \pm \sqrt{7}}{2}$$

Question 16

Suppose you are building a rectangular fence bordering a river with 3,000 ft of fencing available (no fencing required along the river). What is the maximum area you can enclose?

Accepted Answer

$$562,500 sq ft$$

Question 17

Given the cost function $$C(x) = 2x + 4,000$$ and the demand equation $$p = 250 - 2x$$, what is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = (250 - 2x)x - (2x + 4,000)$$

Question 18

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

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$[k, \infty) or$$ $$(-\infty, k]$$ depending on $$a$$

Question 19

Given the graph of $$f(x) = -3x^2$ + 6x + 1$$, what is the maximum value of the function?

Accepted Answer

$$7$$

Quadratic and Polynomial Functions: Concepts, Graphs, and Applications

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