Question

What is the correct form of the quadratic expression g(x)=4x²−28x+49 after completing the square?

A) 4(x−7)²
B) 4(x+7)²
C) 2(x−7)²
D) 2(x+7)²

Answer 1

The correct form of the quadratic expression g(x) after completing the square is: D) (2x - 14)²

Here's how to complete the square for the quadratic expression g(x):

Factor out 4:

g(x) = 4x² - 28x + 49

Move the constant term to the right side:

4x² - 28x = -49

Half the coefficient of the x term:

-28/2 = -14

Square the half of the coefficient:

(-14)² = 196

Add and subtract the constant term squared inside the parentheses:

4x² - 28x + 196 - 196 = -49

Rewrite the left side as a squared term:

(2x - 14)² - 196 = -49

Add 196 to both sides:

(2x - 14)² = 147

Therefore, the correct form of the quadratic expression g(x) after completing the square is: D) (2x - 14)²