Question 1

A football is punted and follows a parabolic path, modeled by the quadratic function $$h(t) = -16t^2$ + 64t + 3$$, where $$h is $$the height in feet and $$t is $$the time in seconds. What is the maximum height the football reaches?

Accepted Answer

$$h = 131$$ feet

Question 2

Which of the following is NOT a polynomial function?

Accepted Answer

$$g(x) = x$$^{1/2}$$ + 4$$

Question 3

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

Accepted Answer

$$(3, 5)$$

Question 4

A company models its profit with the polynomial $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$26$$ thousand dollars at $$x = 2$$ thousand units

Question 5

Which of the following is the standard form of a quadratic function with vertex at $$(4, -1)$$ and passing through the point $$(2, 3)$$?

Accepted Answer

$$f(x) = 1.25(x-4)^2$ - 1$$

Question 6

Divide $$x^2 + 3x - 2$ by x + 1$ using long division. What is the quotient and remainder?

Accepted Answer

Quotient: $$x + 2$$, Remainder: $$-4$$

Question 7

Use synthetic division to divide $$2x^3 - x + 3$ by x - 1$. What is the remainder?

Accepted Answer

$$2$$

Question 8

If a polynomial $$P(x) is $$divided by $$x - 3$$ and the remainder is $$7$$, what is $$P(3)$$?

Accepted Answer

$$7$$

Question 9

Which of the following statements about the Factor Theorem is correct?

Accepted Answer

If $$P(a) = 0$$, then $$x - a is a $$factor of $$P(x)$$

Question 10

Find all real zeros of the polynomial $$f(x) = x^3$ - 4x^2$ - 7x + 10.$$

Accepted Answer

$$x = 1, x = -2, x = 5$$

Question 11

Which of the following is the correct standard form for a complex number?

Accepted Answer

$$a + bi$$

Question 12

What is the result of multiplying $$(2 + 3i)(2 - 3i)$$?

Accepted Answer

$$13$$

Question 13

Solve the quadratic equation $$x^2 + 6x + 10 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = -3 \pm i$$

Question 14

Given $$f(x) = x^4$ - x^3$ + x^2$ - 3x - 6$$, use the Rational Zero Test to list all possible rational zeros.

Accepted Answer

$$\pm1, \pm2, \pm3, \pm6$$

Question 15

If $$f(x) is a $$polynomial with real coefficients and $$3 + 2i is a $$zero, which of the following must also be a zero?

Accepted Answer

$$3 - 2i$$

Question 16

Solve the polynomial inequality $$x^2 - 2x - 3$$ \u003c 0$$. What is the solution set?

Accepted Answer

$$-1 \u003c x \u003c 3$$

Question 17

Find the domain of the expression $$\sqrt{64 - 4x^2$}.$$

Accepted Answer

$$-4 \leq x \leq 4$$

Question 18

A rational function is undefined when:

Accepted Answer

The denominator is zero

Question 19

Which of the following is the correct factorization of $$x^4$$ - $$13x^2 + 36$?

Accepted Answer

$$(x-3)(x+2)(x-2)(x+3)$$

Polynomial and Rational Functions: Precalculus Study Guide

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