Question 1

Which of the following is the correct application of the Zero Product Principle when solving the equation $x^2 - 5x = 0$?

Accepted Answer

Set $x = 0$ or $x - 5 = 0$, so $x = 0$ or $x = 5$

Question 2

What is the solution set for the equation $(x-2)(x-6) = 0$?

Accepted Answer

$\{2, 6\}$

Question 3

A ball is thrown upward and its height in meters after $t$ seconds is given by $h = -4.9t^2 + 19.6t + 1.5$. After how many seconds does the ball hit the ground? (Round to the nearest tenth)

Accepted Answer

$t = 4.1$

Question 4

Which of the following equations can be solved using the square root property?

Accepted Answer

$(x+3)^2 = 16$

Question 5

Solve for $x$: $9x^2 = 81$

Accepted Answer

$x = 3$ or $x = -3$

Question 6

Which of the following is a perfect square trinomial?

Accepted Answer

$x^2 + 6x + 9$

Question 7

What is the solution to $x^2 = -25$?

Accepted Answer

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

Question 8

If $x^2 + 8x + 16 = 0$, what is the value of $x$?

Accepted Answer

$x = -4$

Question 9

Which step is necessary when solving $x^2 - 6x + 9 = 0$ by completing the square?

Accepted Answer

Rewrite as $(x-3)^2 = 0$

Question 10

A rectangular garden has an area of $48$ m$^2$ and its length is $x+4$ meters while its width is $x$ meters. What is the width of the garden?

Accepted Answer

$x = 6$

Question 11

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

Accepted Answer

$\{0, 2\}$

Question 12

Solve for $x$: $(x+5)^2 = 49$

Accepted Answer

$x = 2$ or $x = -12$

Question 13

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

Accepted Answer

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

Question 14

If $x^2 + 2x = 0$, what are the solutions for $x$?

Accepted Answer

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

Question 15

Which of the following is the correct way to solve $x^2 = 12$?

Accepted Answer

$x = \sqrt{12}$ or $x = -\sqrt{12}$

Question 16

A quadratic equation is called a second-degree polynomial equation because:

Accepted Answer

The highest power of $x$ is $2$

Question 17

Which of the following is the correct solution to $4x^2 = 25$?

Accepted Answer

$x = \frac{5}{2}$ or $x = -\frac{5}{2}$

Question 18

If $x^2 + 6x + 9 = 0$, what is the value of $x$?

Accepted Answer

$x = -3$

Question 19

Which of the following is the correct step to complete the square for $x^2 + 4x = 0$?

Accepted Answer

Add $4$ to both sides to get $x^2 + 4x + 4 = 4$

Solving Quadratic Equations: Factoring, Square Roots, and Completing the Square

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