Question

The vertex form of the equation of a parabola is y = 2(x + 3)2 - 5.

What is the standard form of the equation?

A. x = 2y2 + 5y + 9
B. y = 2x2 + 5x + 9
C. y = 4x2 + 4x + 4
D. y = 2x2 + 12x + 13

Answer 1

y = 2(x+3)² - 5

(x+3)² = x(x+3) + 3(x+3) ⇒ x² + 3x + 3x + 9 = x² + 6x + 9

y = 2(x² + 6x + 9) - 5
y = 2x² + 12x + 18 - 5
y = 2x² + 12x + 13 This is the standard form of the equation. Choice D.