Question 1

Which of the following is the correct first step to solve $$x^2 + 6x - 5 = 0$ by completing the square?

Accepted Answer

$$x^2 + 6x = 5$

Question 2

What value should be added to both sides of $$x^2 + 8x = 20$ to complete the square?

Accepted Answer

$$16$$

Question 3

After completing the square for $$x^2 - 4x + 1 = 0$, which equation is correct?

Accepted Answer

$$(x - 2)^2$ = 3$$

Question 4

Which of the following is the solution to $$x^2 + 10x + 21 = 0$ using the completing the square method?

Accepted Answer

$$x = -5 \pm 2$$

Question 5

Given $$x^2 + bx = c$, what is the formula for the value to add to both sides to complete the square?

Accepted Answer

$$\left( \frac{b}{2} \$$right)^2$$

Question 6

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t + 2. $$Using completing the square, what is the vertex form of this equation?

Accepted Answer

$$h = -5(t - 2)^2$ + 22$$

Question 7

Which step is necessary after writing $$x^2 + 4x = 12$ to complete the square?

Accepted Answer

Add $$4 to $$both sides (since $$(\frac{4}{2})^2$ = 4)$$

Question 8

If you complete the square for $$x^2 - 6x + 5 = 0$, what is the resulting equation before taking the square root?

Accepted Answer

$$(x - 3)^2$ = 4$$

Question 9

Which property allows you to solve $$(x + a)^2$ = b by $$taking the square root of both sides?

Accepted Answer

Square Root Property

Question 10

A quadratic equation $$x^2 + 12x + k = 0$ has exactly one real solution. What is the value of k$?

Accepted Answer

$$36$$

Question 11

Which of the following best describes the purpose of completing the square?

Accepted Answer

To rewrite a quadratic equation in the form $$(x + a)^2$ = b$$ for easier solving

Question 12

Solve $$x^2 + 2x - 8 = 0$ by completing the square. What are the solutions?

Accepted Answer

$$x = -1 \pm 3$$

Question 13

Which of the following is the correct step after $$x^2 + 4x = -1$ when completing the square?

Accepted Answer

$$x^2 + 4x + 4 = -1 + 4$

Question 14

If $$x^2 + 14x + 49 = 0$, what is the solution for x$?

Accepted Answer

$$x = -7$$

Question 15

Which of the following real-world scenarios can be modeled by completing the square?

Accepted Answer

Finding the maximum height of a projectile

Completing the Square: Solving Quadratic Equations

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