Question 1

Simplify $$(4 - 8i)(8 - 3i)$$ and write your answer in the form $$a + bi$$, where $$a$$ and $$b$$ are real numbers.

Accepted Answer

$$8 - 76i$$

Question 2

What is the value of $$(4i)^4$$?

Accepted Answer

$$256$$

Question 3

Solve the equation $$x^2 - 10x + 25 = 36$.

Accepted Answer

$$x = 11, x = -1$$

Question 4

Solve $$5x^2 = 35x$.

Accepted Answer

$$x = 0, x = 7$$

Question 5

Solve $$(7x - 9)(7x - 5) = 0.$$

Accepted Answer

$$x = \frac{9}{7}, x = \frac{5}{7}$$

Question 6

Solve $$x^2 - 12x + 35 = 0$.

Accepted Answer

$$x = 7, x = 5$$

Question 7

Solve $$3x^3$$ + $$x^2 - 12x - 4 = 0$.

Accepted Answer

$$x = -2, x = 2, x = -\frac{1}{3}$$

Question 8

Given the graph of $$y = x^2$ - 5x + 6$$, what are the $$x-$$intercepts?

Accepted Answer

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

Question 9

Solve by completing the square: $$x^2 + 10x + 14 = 0$.

Accepted Answer

$$x = -5 \pm \sqrt{11}$$

Question 10

Use the quadratic formula to solve $$x^2 + 35 = 5x$.

Accepted Answer

$$x = \frac{5}{2} \pm \frac{\sqrt{115}}{2}i$$

Question 11

Consider only the discriminant $$b^2 - 4ac$ for x^2$ + 2x + 2 = 0. $$What type of solutions exist?

Accepted Answer

Two different imaginary-number solutions

Question 12

The length of a rectangle is three inches more than the width. The area of the rectangle is $$378$$ square inches. What is the width?

Accepted Answer

$$18$$ inches

Question 13

Find the vertex of the parabola $$f(x) = 2x^2$ - 4x - 2.$$

Accepted Answer

$$(1, -4)$$

Question 14

Find the axis of symmetry for $$f(x) = -2x^2$ + 11x + 2.$$

Accepted Answer

$$x = \frac{11}{4}$$

Question 15

Determine whether there is a maximum or minimum value for $$f(x) = -x^2$ + 9x - 5$$ and find that value.

Accepted Answer

Maximum: $$\frac{61}{4}$$

Question 16

Find the range of $$f(x) = x^2$ - 5x + 6.$$

Accepted Answer

$$\left[ -\frac{1}{4}, \infty \right)$$

Question 17

If $$m$$ varies directly as $$p$$ and $$m = 54$$ when $$p = 6$$, what is the equation of variation?

Accepted Answer

$$m = 9p$$

Question 18

If $$y$$ varies inversely as $$x$$ and $$y = 80$$ when $$x = 8$$, what is the equation of variation?

Accepted Answer

$$y = \frac{10}{x}$$

Question 19

The time $$T$$ necessary to make an enlargement of a photo negative varies directly as the area $$A of $$the enlargement. If $$80$$ seconds are required to make a $$5-by$$-$$4$$ enlargement, find the time required for a $$6-by$$-$$5$$ enlargement.

Accepted Answer

$$120$$ seconds

College Algebra Exam Study Guide: Quadratics, Polynomials, and Variation

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