Question

Complete the square for the quadratic part of the equation 3x² +12x+4y−8=0 to obtain the standard form of the equation. What is the correct form?

a) 3(x+2)² +4y−20=0
b) 3(x+2)² −12+4y−8=0
c) 3(x² +4x+4)+4y−8=0
d) 3(x+2)²+12x+4y−8=0

Answer 1

To complete the square, factor out the coefficient of x², take half of the coefficient of x and square it to obtain the constant term, add and subtract the squared constant term to the expression, and rearrange it to obtain the standard form.

Step-by-step explanation:

To complete the square for the quadratic part of the equation 3x² + 12x + 4y - 8 = 0, we will focus on the terms involving x. We want to rewrite the quadratic expression as a perfect square trinomial.

1. Factor out the coefficient of x²: 3(x² + 4x)
2. Take half of the coefficient of x (which is 4) and square it to obtain the constant term: (4/2)² = 4
3. Add and subtract the squared constant term to the expression: 3(x² + 4x + 4 - 4)
4. Simplify the expression and rearrange it to obtain the standard form: 3(x + 2)² + 4y - 20 = 0

Therefore, the correct form of the equation is a) 3(x+2)² +4y−20=0.