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. \\(y = 2x^2 + 5x + 9\\)
b. \\(y = 2x^2 + 12x + 13\\)
c. \\(y = 4x^2 + 4x + 4\\)
d. \\(x = 2y^2 + 5y + 9\\)

Explanation:

Expand the squared binomial

$$ (x+3)^2 = x^2 + 6x + 9 $$

Multiply by the leading coefficient

$$ 2(x+3)^2 = 2(x^2 + 6x + 9) = 2x^2 + 12x + 18 $$

Subtract the constant term

$$ y = (2x^2 + 12x + 18) - 5 = 2x^2 + 12x + 13 $$

Answer:

• A. \(y = 2x^2 + 5x + 9\)
• B. \(y = 2x^2 + 12x + 13\) (Correct answer)
• C. \(y = 4x^2 + 4x + 4\)
• D. \(x = 2y^2 + 5y + 9\)