Question 1

Solve the following equation for $$x$$: $$3x + 5 = 2x - 7.$$

Accepted Answer

$$x = -12$$

Question 2

Which of the following is the solution set for $$x^2 - 4x + 3 = 0$?

Accepted Answer

$$x = 1, 3$$

Question 3

Given the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$, what is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 4

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 5

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$

Question 6

Which of the following describes the solution set for $$x^2 + 4 = 0$?

Accepted Answer

No real solution

Question 7

If $$f(x) = x^2$ - 2x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, 0)$$

Question 8

Given the function $$f(x) = 2x^2$ - 8x + 6$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-2$$

Question 9

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

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

Question 10

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$18$$

Question 11

Which of the following is the solution to the inequality $$x^2 - 4x$$ \u003e 0$$?

Accepted Answer

$$x  4$$

Question 12

If $$f(x) = x^2$ - 6x + 8$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 2 or$$ $$x = 4$$

Question 13

Which of the following is the correct solution for $$2x^2 + 3x - 2 = 0$?

Accepted Answer

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

Question 14

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

Accepted Answer

$$x = 2$$

Question 15

Which of the following is the correct solution for $$x^2 + 2x + 1 = 0$?

Accepted Answer

$$x = -1$$

Question 16

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

Accepted Answer

$$x = -2, 4$$

Question 17

Which of the following is the correct solution for $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2, 3$$

Question 18

If $$f(x) = x^2$ + 2x + 2$$, what is the minimum value of $$f(x)$$?

Accepted Answer

Question 19

Which of the following is the correct solution for $$x^2 - 2x - 3 = 0$?

Accepted Answer

$$x = 3, -1$$

College Algebra Study Notes: Equations, Functions, and Graphs

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