Quiz about Solving Quadratic Equations by Completing the Squares

Question 1

Solve by completing the square.
y² + 10y = -9

Accepted Answer

-1 and -9

Answer

1 and -12

Answer

1 and -9

Answer

1 and -1

Question 2

Question 2.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 3

Complete the square for: v² - 18v + 87 = 7

Accepted Answer

(v - 9)² - 1

Answer

(v + 9)² - 1

Answer

(v + 9)² + 1

Answer

(v - 9)² + 1

Question 4

A rocket's trajectory is modeled by the equation $$x^2 - 12x + 27 = 0$$ , where $$x$$ represents the time in seconds after launch, and the equation gives its altitude. To predict the time when the rocket will reach its peak altitude, complete the square.

Accepted Answer

$$x = 6 \pm \sqrt{9}$$

Answer

$$x = 6 \pm \sqrt{12}$$

Answer

$$x = 6 \pm \sqrt{15}$$

Answer

$$x = 6 \pm \sqrt{18}$$

Question 5

Question 5.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 6

A farmer is planning to create a rectangular enclosure for her sheep. She wants the area of the enclosure to be represented by the quadratic equation $$2x^2 - 8x - 10 = 0$$ , where $$x$$ is the length of the enclosure in meters. Help her determine the possible lengths of the enclosure by completing the square.

Accepted Answer

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

Answer

$$x = 2 \pm \sqrt{5}$$

Answer

$$x = 4 \pm \sqrt{12}$$

Answer

$$x = 4 \pm \sqrt{5}$$

Question 7

Question 7.

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 8

John is planning to build a rectangular garden and he wants the area of the garden to be represented by the quadratic equation $$x^2 + 10x + 16 = 0$$ . To determine the possible dimensions (x) of the garden, he needs to solve this equation. Complete the square to find the value of x.

Accepted Answer

$$x = -5 \pm \sqrt{9}$$

Answer

$$x = -5 \pm \sqrt{1}$$

Answer

$$x = 5 \pm \sqrt{9}$$

Answer

$$x = 5 \pm \sqrt{1}$$

Question 9

Question 9.

Accepted Answer

G

Answer

F

Answer

H

Answer

I

Question 10

(x + 1) ² + 3 = 15

Accepted Answer

$$\left\{-1\pm2\ \ \sqrt[]{3}\right\}$$

Answer

$$\left\{1\pm3\ \ \sqrt[]{2}\right\}$$

Answer

$$\left\{-7,5\right\}$$

Answer

$$\left\{-3\ \sqrt[]{3},\ 1\ \sqrt[]{3}\right\}$$

Solving Quadratic Equations by Completing the Squares

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