Question 1

Which of the following is the correct completed square form of the quadratic expression $$x^2 + 6x - 4$?

Accepted Answer

$$ (x + 3)^2$ - 13 $$

Question 2

What is the completed square form of $$x^2 - 8x + 7$?

Accepted Answer

$$ (x - 4)^2$ - 9 $$

Question 3

Given the quadratic equation $$x^2 + 4x - 12 = 0$, what are the solutions using the completing the square method?

Accepted Answer

$$ x = 2, x = -6 $$

Question 4

What is the completed square form of $$x^2 + 5x + 3$?

Accepted Answer

$$ \left( x + \frac{5}{2} \$$right)^2$$ - \frac{13}{4} $$

Question 5

For the quadratic expression $$3x^2 - 9x + 50$, what is the completed square form?

Accepted Answer

$$ 3 \left( x - \frac{3}{2} \$$right)^2$$ + \frac{173}{12} $$

Question 6

What is the first step when completing the square for $$5x^2 + 10x + 15$?

Accepted Answer

Factor out the coefficient of $$x^2 to $$get $$5(x^2 + 2x + 3$$)$$

Question 7

Which of the following is the completed square form of $$x^2 + 10x - 1$?

Accepted Answer

$$ (x + 5)^2$ - 26 $$

Question 8

Solve $$x^2 + 6x = 4$ by completing the square. What are the solutions?

Accepted Answer

$$ x = -3 \pm \sqrt{13} $$

Question 9

Which of the following best describes the process of completing the square for $$ax^2 + bx + c$ when a$$ 
eq 1$$?

Accepted Answer

Factor out $$a$$, complete the square for the quadratic inside the parentheses, then adjust the constant term

Question 10

What is the completed square form of $$2x^2 + 4x - 8$?

Accepted Answer

$$ 2 \left( (x + 1)^2$ - 5 \right) $$

Question 11

A quadratic equation models the height $$h (in $$meters) of a projectile as $$h = -2x^2$ + 8x + 5. $$What is the completed square form of this expression?

Accepted Answer

$$ -2 \left( (x - 2)^2$ - \frac{9}{2} \right) $$

Question 12

Which of the following is the completed square form of $$x^2 - x - 1$?

Accepted Answer

$$ \left( x - \frac{1}{2} \$$right)^2$$ - \frac{5}{4} $$

Question 13

If you are given $$x^2 + 2x + 5$, what is the completed square form?

Accepted Answer

$$ (x + 1)^2$ + 4 $$

Question 14

Which of the following is the completed square form of $$x^2 + x + 1$?

Accepted Answer

$$ \left( x + \frac{1}{2} \$$right)^2$$ + \frac{3}{4} $$

Question 15

What is the completed square form of $$x^2 - 2x + 6$?

Accepted Answer

$$ (x - 1)^2$ + 5 $$

Question 16

A quadratic equation $$x^2 + 4x - 8 = 0$ is solved by completing the square. What are the solutions?

Accepted Answer

$$ x = -2 \pm \sqrt{12} $$

Question 17

Which of the following is the completed square form of $$x^2 + 6x + 8$?

Accepted Answer

$$ (x + 3)^2$ - 1 $$

Completing the Square: Quadratic Expressions and Equations

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