Quiz On Completing The Square
This quiz covers all areas of completing the square
Questions and Answers
- 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
Correct Answer
C. Divide by 4Explanation
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.Rate this question:
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- 2.
The goal of completing the square is to create a
Correct Answer
perfect square trinomialExplanation
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.Rate this question:
- 3.
X^2-8x+16 would factor into...
- A.
(x-4)^2
- B.
(x+4)^2
- C.
(x+8)^2
- D.
(x-8)^2
Correct Answer
A. (x-4)^2Explanation
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.Rate this question:
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- 4.
What term would make x^2+6x a perfect square trinomial? (you need to include the sign)
Correct Answer
+9Explanation
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.Rate this question:
- 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
Correct Answer
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.Rate this question:
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Current Version
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Mar 22, 2023Quiz Edited by
ProProfs Editorial Team -
May 04, 2010Quiz Created by
Stephenpate
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