Quiz On Completing The Square
This quiz focuses on the algebraic technique of completing the square. It assesses understanding through problems that require forming perfect square trinomials and solving quadratic equations, enhancing skills crucial for academic success in mathematics.
- 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:
-
- 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:
-
- 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:
-
Quiz Review Timeline +
Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.
-
Current Version
-
Jul 24, 2024Quiz Edited by
ProProfs Editorial Team -
May 04, 2010Quiz Created by
Stephenpate