Question 1

Which of the following best describes the graph of the quadratic function $$f(x) = -2(x-3)^2$ + 5$$?

Accepted Answer

It opens downward, has vertex at $$(3, 5)$$, and has a maximum value of $$5.$$

Question 2

Given the quadratic equation $$2x^2 - x = 3$, what are the solutions?

Accepted Answer

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

Question 3

Which of the following is the factored form of $$x^2 + 2x - 15$?

Accepted Answer

$$(x + 5)(x - 3)$$

Question 4

A model rocket is launched from a hill. Its height after $$t$$ seconds is given by $$s(t) = -16t^2$ + 100t + 20. At $$what time does the rocket reach its maximum height, and what is that height?

Accepted Answer

At $$t = 3.125$$ seconds, maximum height is $$176.25$$ feet.

Question 5

Which of the following statements about the discriminant $$b^2 - 4ac$ of a quadratic equation ax^2$ + bx + c = 0 is $$correct?

Accepted Answer

If the discriminant is negative, there are two complex conjugate solutions.

Question 6

Solve the equation $$|x - 3| = 7.$$

Accepted Answer

$$x = 10 or$$ $$x = -4$$

Question 7

A farmer has 300 feet of fencing to enclose a rectangular region bordering a barn, with a fence dividing the region into two equal pens. If $$x is $$the width of each pen, which equation models the total area $$A(x)$$?

Accepted Answer

$$A(x) = x(300 - 3x)$$

Question 8

Which of the following is the correct solution to the radical equation $$\sqrt{3x + 1} = 4$$?

Accepted Answer

$$x = 5$$

Question 9

What is the sum and product of the roots of the quadratic equation $$x^2 - 9x + 18 = 0$?

Accepted Answer

Sum: $$9$$, Product: $$18$$

Question 10

Which of the following is the correct factored form of $$2x^2 + 10x + 24$?

Accepted Answer

$$2(x^2 + 5x + 12$$)$$

Question 11

If $$f(x) = x^2$ - 4x - 5$$, what are the $$x-$$intercepts of the graph?

Accepted Answer

$$x = -1$$ and $$x = 5$$

Question 12

Which of the following is the correct solution set for $$|2x - 6| \u003c 8$$?

Accepted Answer

$$-1 \u003c x \u003c 7$$

Question 13

A tech company’s cost function is $$C(x) = 0.5x^2$ - 40x + 1200$$, where $$x is $$the number of smartphones produced (in hundreds). What is the minimum cost and how many smartphones should be produced to achieve it?

Accepted Answer

Produce $$40$$ hundred smartphones for a minimum cost of $$400$$ dollars.

Question 14

Which of the following is the correct solution to the equation $$x^2 + 13 = 0$?

Accepted Answer

$$x = \pm \sqrt{13}i$$

Question 15

Which of the following is the correct form for the vertex of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$(\frac{-b}{2a}, f(\frac{-b}{2a}))$$

Question 16

Solve the rational equation $$\frac{x-8}{3} + \frac{x-3}{2} = 0.$$

Accepted Answer

$$x = 5$$

Question 17

Which of the following is the correct solution to $$x^4$$ - $$5x^2 + 4 = 0$?

Accepted Answer

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

Question 18

Which of the following is the correct solution to $$|x| = -3$$?

Accepted Answer

No solution

College Algebra Study Guide: Quadratic, Rational, Radical, and Absolute Value Equations

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