Question

Which expression is equivalent to 2x2−x+1/8A

2(x−12)2

B
2(x−14)2

C
2(x−18)2

D
2(x−116)2

Answer 1

Answer: D. 2(x−1/16)^2

Explanation:

To find the equivalent expression in the given options, we'll complete the square:

1. First, let's focus on the x^2 term. Factor out the 2:

2(x^2 - (1/2)x) + 1/8

2. Now, we'll complete the square inside the parentheses by adding and subtracting the appropriate square term:

To determine this term, take half of the x coefficient (1/2) and square it: (1/4)^2 = 1/16.

So, the expression becomes:

2(x^2 - (1/2)x + 1/16 - 1/16) + 1/8

3. Now, rewrite the expression with the completed square:

2((x - 1/4)^2 - 1/16) + 1/8

4. Distribute the 2:

2(x - 1/4)^2 - 2(1/16) + 1/8

5. Simplify the expression:

2(x - 1/4)^2 - 1/8 + 1/8

6. The last two terms cancel each other out, and we are left with:

2(x - 1/4)^2

This expression is equivalent to option D:

D. 2(x−1/16)^2