Quiz about Solving Quadratics by Completing the Square

Question 1

What do you do to the b value to correctly complete the square?

Accepted Answer

divide it by 2 and square the result

Answer

square it

Answer

divide it by 2 and take the square root of the result

Answer

divide it by 2 only

Question 2

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

Accepted Answer

the -4x

Answer

the 9

Answer

the x2

Question 3

(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

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

Question 4

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 5

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 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

Solve the following quadratic equation by completing the square:

2x² -3x = -4

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 8

Solve. x² + 4x - 16 = 0

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 9

John is trying to calculate the dimensions of a garden that is shaped like a quadratic equation $$x^2 + 6x + 8 = 0$$ . Help him by completing the square.

Accepted Answer

$$x = -3 \pm \sqrt{1}$$

Answer

$$x = -3 \pm \sqrt{7}$$

Answer

$$x = 3 \pm \sqrt{1}$$

Answer

$$x = 3 \pm \sqrt{7}$$

Solving Quadratics by Completing the Square

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