Question 1

Which of the following is the correct factorization of $$a^2$$ - $$b^2$$?

Accepted Answer

$$a^2$$ - $$b^2 = (a + b)(a - b$$)$$

Question 2

Given the quadratic equation $$4x^2 - 3x - 5 = 0$, what are the solutions using the quadratic formula?

Accepted Answer

$$x = \dfrac{3 \pm \sqrt{71}}{8}$$

Question 3

If $$a  0$$, which of the following is true according to the properties of inequalities?

Accepted Answer

$$ac \u003c bc$$

Question 4

What is the result of $$\sqrt{-a}$$ for $$a \u003e 0$$?

Accepted Answer

$$\sqrt{-a} = i\sqrt{a}$$

Question 5

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

Accepted Answer

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

Question 6

If $$a \u003c b$$ and $$c \u003c 0$$, what happens to the inequality when both sides are multiplied by $$c$$?

Accepted Answer

$$ac \u003e bc$$

Question 7

A chemical reaction is modeled by the equation $$x^2 - 6x + 9 = 0$. What is the concentration of x$ at equilibrium?

Accepted Answer

$$x = 3$$

Question 8

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

Accepted Answer

$$x = \pm 2i$$

Question 9

A medical dosage calculation requires solving $$2x^2 - 8x = 0$. What is the correct dosage value(s) for x$?

Accepted Answer

$$x = 0 or$$ $$x = 4$$

Question 10

If $$a \u003c b$$, which of the following is always true after adding $$c to $$both sides?

Accepted Answer

$$a + c \u003c b + c$$

Question 11

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward: $$h = -4.9t^2$ + 20t + 1.5. At $$what time $$t$$ does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 12

Which of the following is the correct solution for $$x in$$ $$x^2 = 25$?

Accepted Answer

$$x = 5 or$$ $$x = -5$$

Question 13

If $$a \u003c b$$ and $$c = 0$$, what is the result of multiplying both sides by $$c$$?

Accepted Answer

$$ac = bc = 0$$

Question 14

A historical event is modeled by the equation $$t^2 - 10t + 21 = 0$. What are the possible years t$ when the event occurred?

Accepted Answer

$$t = 3 or$$ $$t = 7$$

Question 15

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

Accepted Answer

$$x = -1$$

Question 16

If you divide both sides of an inequality by a negative number, what must you do to the inequality sign?

Accepted Answer

Reverse the inequality sign

Question 17

Which of the following is the correct factorization of $$x^2 + 6x + 9$?

Accepted Answer

$$(x + 3)^2$

Question 18

A population model is given by $$n^2 - 16 = 0$. What are the possible population sizes n$?

Accepted Answer

$$n = 4 or$$ $$n = -4$$

Question 19

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

Accepted Answer

$$x = 0 or$$ $$x = 2$$

Key Precalculus Concepts: Properties of Inequality, Quadratic Equations, and Factoring

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