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

Study Guide - Practice Questions

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