Question

Don completes the square for the equation x^2 + 6x + 3 = 0. Which of the following equations reveals the vertex of the parabola?

Answer 1

x² + 6x + 3 = 0

y = x² + 6x + 3
y - 3 = x² + 6x

6x ⇒ 6x / 2x = 3 ⇒ 3² = 9

y - 3 + 9 = x² + 6x + 9
y + 6 = (x+3)²
y = (x+3)² - 6

vertex of the parabola is (x+3)²

y = (x+3)(x+3) - 6
y = x(x+3)+3(x+3) - 6
y = x² + 3x + 3x + 9 - 6
y = x² + 6x + 3