Question 1

Which of the following is the vertex of the parabola given by $$f(x) = 2(x + 1)^2$ - 3$$?

Accepted Answer

$$( -1, -3 )$$

Question 2

Given $$f(x) = x^2$ - 6x + 8$$, what are the $$x-$$intercepts of the graph?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 3

If $$f(x) = \dfrac{4x}{x+2}$$ and $$g(x) = \dfrac{7}{x+5}$$, what is $$(f+g)(1)$$?

Accepted Answer

Question 4

Given $$f(x) = x^2$ - 4x + 5$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 5

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

Accepted Answer

Question 6

Given $$f(x) = x^3$ - 3x^2$ + 2x$$, use the Rational Zeros Theorem to determine which of the following is a possible rational zero.

Accepted Answer

$$x = 1$$

Question 7

If $$f(x) = x^2$ + 4x + 5$$ and $$g(x) = x - 2$$, what is $$(f \circ g)(3)$$?

Accepted Answer

$$13$$

Question 8

A line passes through $$(2, -5)$$ and $$(1, -4). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -x - 3$$

Question 9

Given $$f(x) = x^3$ - 2x^2$ - 3x + 6$$, and knowing $$x = -1 is a $$zero, which of the following is a factor of $$f(x)$$?

Accepted Answer

$$x + 1$$

Question 10

Use synthetic division to evaluate $$f(2)$$ for $$f(x) = x^3$ - 4x^2$ + 5x - 2.$$

Accepted Answer

$$4$$

Question 11

Which of the following is the equation of the line passing through $$(9, 4)$$ and parallel to $$5x - 7y = 11$$?

Accepted Answer

$$5x - 7y = 29$$

Question 12

Given $$f(x) = x^2$ - 4x + 5$$, what is the $$y-$$intercept?

Accepted Answer

$$5$$

Question 13

If $$f(x) = x^3$ + 2x^2$ - x - 2$$, and $$x = 1 is a $$zero, factor $$f(x)$$ completely.

Accepted Answer

$$(x - 1)(x^2$ + 3x + 2)$$

Question 14

Find all zeros of $$f(x) = x^3$ - 6x^2$ + 11x - 6.$$

Accepted Answer

$$x = 1, 2, 3$$

Question 15

A chemical reaction's rate is modeled by $$R(t) = -t^2$ + 6t + 5$$, where $$t is $$time in seconds. When does the reaction reach its maximum rate?

Accepted Answer

$$t = 3$$

Question 16

Given $$f(x) = x^2$ - 4x + 5$$ and $$g(x) = x + 2$$, what is $$(f - g)(1)$$?

Accepted Answer

$$3$$

Question 17

Divide $$x^4$$ + $$3x^3$$ - $$10x^2 + 13x + 20$ by x + 3$. What is the remainder?

Accepted Answer

$$-7$$

Question 18

Find all zeros of $$f(x) = x^4$ + 10x^2$ + 25$$ given that $$x = i is a $$zero.

Accepted Answer

$$x = 0, 5i, -5i$$

Question 19

Given $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, use the Remainder Theorem to find $$f(2).$$

Accepted Answer

$$4$$

College Algebra Test #2 Review – Step-by-Step Guidance

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