Question 1

Which of the following is NOT a method for solving a quadratic equation as listed in the study materials and the image provided?

Accepted Answer

Synthetic Division

Question 2

Given the quadratic equation $$2x^2 - 8x - 24 = 0$, which is the correct first step when solving by completing the square?

Accepted Answer

Divide both sides by 2 to get $$x^2 - 4x = 12$

Question 3

Which of the following expressions is a quadratic trinomial?

Accepted Answer

$$2x^2 + 7x - 5$

Question 4

What is the solution set for $$9x^2 = 16$ using the square root property?

Accepted Answer

$$x = \pm \frac{4}{3}$$

Question 5

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what can you conclude about the solutions?

Accepted Answer

There are two distinct imaginary solutions

Question 6

Which of the following is the correct factorization of $$9x^2 - 49$?

Accepted Answer

$$(3x - 7)(3x + 7)$$

Question 7

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t + 1. $$When will the ball hit the ground? (Solve for $$t$$ when $$h = 0$$ using the quadratic formula.)

Accepted Answer

$$t = 4.04$$ and $$t = -0.04$$

Question 8

Which of the following best describes the graph of a quadratic equation with a discriminant equal to zero?

Accepted Answer

The graph touches the $$x-$$axis at one point

Question 9

Solve the equation $$x^2 - 2x - 3 = 0$ by factoring. What are the solutions?

Accepted Answer

$$x = -1, 3$$

Question 10

Which of the following is the correct application of the zero-product principle?

Accepted Answer

If $$(x-1)(x+2) = 0$$, then $$x = 1 or$$ $$x = -2$$

Question 11

Given the equation $$x^2 + 6x + 8 = 0$, which method would be most efficient to solve it?

Accepted Answer

Factoring

Question 12

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 13

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). For what values of $$x$$ does the company break even? (Solve for $$P = 0.)$$

Accepted Answer

$$x = 1.53$$ and $$x = 5.22$$

Question 14

Which of the following is the correct way to factor $$12a^2$$ - $$27b^2$$ completely?

Accepted Answer

$$3(2a - 3b)(2a + 3b)$$

Question 15

If $$x^2 = -9$, what are the solutions?

Accepted Answer

$$x = 3i, -3i$$

Quadratic Equations: Methods of Solution and Properties

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