Question 1

Simplify the following complex number: $$\sqrt{-36}$$

Accepted Answer

$$6i$$

Question 2

What is the result of $$(12 + 5i) - (20 + 6i)$$?

Accepted Answer

$$-8 - i$$

Question 3

Solve the quadratic equation $$2x^2 + x - 10 = 0$ using the quadratic formula.

Accepted Answer

$$x = 2,\ x = -2.5$$

Question 4

Solve the equation $$x^2 - 6x = -11$.

Accepted Answer

$$x = 3 \pm 2$$

Question 5

A ball is thrown upward from a building 25 meters tall with a vertical velocity of 30 m/sec. Its height after $$t$$ seconds is $$h(t) = -5t^2$ + 30t + 25. $$How long will it take for the ball to hit the ground?

Accepted Answer

$$t = 6.13$$ seconds

Question 6

Given the function $$f(x) = -2|x + 3| - 1$$, which of the following describes its transformations?

Accepted Answer

Reflection over x-axis, vertical stretch by 2, left 3 units, down 1 unit

Question 7

Solve the radical equation $$\sqrt{x} + 10 = x - 2.$$

Accepted Answer

$$x = 16$$

Question 8

Which of the following is the equation of a square root function reflected over the x-axis, shifted 2 units right, and 5 units down?

Accepted Answer

$$f(x) = -\sqrt{x - 2} - 5$$

Question 9

For the quadratic function $$f(x) = x^2$ - 6x + 5$$, what is the vertex?

Accepted Answer

$$(3, -4)$$

Question 10

Use the remainder theorem to determine if $$x = -1 is a $$zero of $$f(x) = x^3$ - 2x^2$ + 7x - 6.$$

Accepted Answer

No, because $$f(-1) = -16$$

Question 11

Find all zeros and their multiplicities for $$g(x) = x(x - 4)(x - 9)^2$.

Accepted Answer

0 (1), 4 (1), 9 (2)

Question 12

Given $$f(x) = (x - 2)(x - 3)(x + 1)$$, what is the degree and leading coefficient?

Accepted Answer

Degree: 3, Leading coefficient: 1

Question 13

For the rational function $$f(x) = \frac{3x - 3}{x + 1}$$, what is the vertical asymptote?

Accepted Answer

$$x = -1$$

Question 14

For the rational function $$g(x) = \frac{x + 6}{x - 3}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 1$$

Question 15

Solve the quadratic equation $$(x - 2)^2$ = -16.$$

Accepted Answer

$$x = 2 \pm 4i$$

Question 16

Which of the following is the axis of symmetry for $$f(x) = x^2$ - 6x + 5$$?

Accepted Answer

$$x = 3$$

Question 17

If a 65-foot ladder is leaned against a wall and the base is 63 feet from the wall, how high up the wall does the ladder reach?

Accepted Answer

$$16$$ feet

Question 18

Which of the following is the y-intercept of $$f(x) = (x - 1)(x - 5)(x + 1)^2$?

Accepted Answer

$$(0, 5)$$

Question 19

For the function $$h(x) = \frac{3}{(x - 1)^2$}$$, what is the vertical asymptote?

Accepted Answer

$$x = 1$$

College Algebra Midterm & Unit Exam Review – Step-by-Step Guidance

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