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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