Quiz On Completing The Square

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Stephenpate
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Questions: 5 | Attempts: 1,407

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This quiz covers all areas of completing the square

• 1.

What is the first thing that should be done to complete the square on 4x^2+8x+16=0

• A.

Subtract 16 from both sides

• B.

Divide 8 by 2 and square it

• C.

Divide by 4

• D.

Factor

C. Divide by 4
Explanation
To complete the square on the given quadratic equation, the first step is to divide the entire equation by the coefficient of x^2, which is 4. This step is necessary to make the coefficient of x^2 equal to 1, which allows for easier completion of the square.

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• 2.

The goal of completing the square is to create a

perfect square trinomial
Explanation
Completing the square is a method used to rewrite a quadratic expression in the form of a perfect square trinomial. By adding and subtracting a constant term to the quadratic expression, we can create a perfect square trinomial with a square term and a constant term. This allows us to easily factorize the quadratic expression and solve for its roots. Therefore, the goal of completing the square is to transform the quadratic expression into a perfect square trinomial.

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• 3.

X^2-8x+16 would factor into...

• A.

(x-4)^2

• B.

(x+4)^2

• C.

(x+8)^2

• D.

(x-8)^2

A. (x-4)^2
Explanation
The given quadratic expression can be factored into (x-4)^2. This is because the expression follows the pattern of a perfect square trinomial, where the first term is the square of the binomial's first term (x^2), the last term is the square of the binomial's second term (16), and the middle term is twice the product of the binomial's terms (-8x). Therefore, the correct factored form is (x-4)^2.

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• 4.

What term would make x^2+6x a perfect square trinomial? (you need to include the sign)

+9
Explanation
Adding +9 to x^2+6x would make it a perfect square trinomial because if we factor x^2+6x+9, it can be written as (x+3)(x+3), which is the square of (x+3). Therefore, +9 is the correct term to make x^2+6x a perfect square trinomial.

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• 5.

What would need to be done next in order to complete the square for x^2-8x    =10?

• A.

Move 10

• B.

Factor

• C.

Take half of 8 and square it.

• D.

Factor out an x

C. Take half of 8 and square it.
Explanation
To complete the square for the given equation, x^2-8x = 10, we need to take half of the coefficient of x (which is 8) and square it. Taking half of 8 gives us 4, and squaring it gives us 16. Thus, we need to add 16 to both sides of the equation to complete the square.

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• Current Version
• Jul 24, 2024
Quiz Edited by
ProProfs Editorial Team
• May 04, 2010
Quiz Created by
Stephenpate

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