Question 1

Simplify $$(4 + 3i) - (-7 + 5i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$11 + 8i$$

Question 2

Multiply $$(3 - 5i)(8 - 2i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$34 - 46i$$

Question 3

Solve the quadratic equation $$x^2 - 8x + 15 = 0$ by factoring. What are the solutions?

Accepted Answer

$$x = 3$$ and $$x = 5$$

Question 4

For the function $$f(x) = x^2$ - 8x + 12$$, what is the vertex of the parabola?

Accepted Answer

$$(4, -4)$$

Question 5

A ball is thrown upward from a height of 192 feet at 64 ft/sec. Its height is given by $$S(t) = 192 + 64t - 16t^2$. After how many seconds is the ball at a height of 240 feet?

Accepted Answer

$$t = 1$$ 	ext{ or } t = 3$

Question 6

A fourth-grade class wants to enclose a rectangular garden using 32 ft of fencing, with the school as one side. What is the maximum area that can be enclosed?

Accepted Answer

$$128$$ 	ext{ square feet}$

Question 7

Solve $$x^2 - 9 = 4x$. What are the solutions?

Accepted Answer

$$x = 7$$ 	ext{ and } x = -1$

Question 8

For the function $$g(x) = x^2$ + 2x + 5$$, what are the $$x-$$intercepts?

Accepted Answer

There are no real $$x-$$intercepts

Question 9

Solve the equation $$\sqrt{1 - 2x} = 3. $$Which solution(s) are valid?

Accepted Answer

$$x = -4$$

Question 10

Solve the absolute value inequality $$|3x + 4| \u003c 13. $$Express your answer in interval notation.

Accepted Answer

$$(-\frac{17}{3}, 3)$$

Question 11

Solve the equation $$|4x - 3| + 1 = 7. $$What are the solutions?

Accepted Answer

$$x = 2$$ 	ext{ or } x = -1$

Question 12

Solve the rational equation $$\frac{2}{x-1} = \frac{3}{x+2}. $$What are the solutions?

Accepted Answer

$$x = -7$$

Question 13

Which of the following is the correct simplification of $$\frac{5}{2 + 3i} in $$the form $$a + bi$$?

Accepted Answer

$$\frac{10}{13} - \frac{15}{13}i$$

Question 14

Solve the quadratic equation $$x^2 - 2x + 5 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = 1 + 2i$$ 	ext{ and } x = 1 - 2i$

Question 15

For the function $$f(x) = x^2$ - 8x + 12$$, does the parabola open upward or downward?

Accepted Answer

Upward

Question 16

Solve the absolute value inequality $$|5 - 2x| \geq 10. $$Express your answer in interval notation.

Accepted Answer

$$(-\infty, -2.5] \cup [7.5, \infty)$$

Question 17

Solve $$4x^2 - 32 = 0$. What are the solutions?

Accepted Answer

$$x = 2$$ 	ext{ and } x = -2$

Question 18

For the function $$g(x) = x^2$ + 2x + 5$$, what is the vertex?

Accepted Answer

$$(-1, 4)$$

Question 19

Solve the equation $$x^4$$ - $$8x^2 - 9 = 0$. Which solutions are valid?

Accepted Answer

$$x = 3$$, $$x = -3$$, $$x = 1$$, $$x = -1$$

College Algebra Exam 3 Study Guide – Step-by-Step Guidance

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