Question

question 8 of 10

the vertex form of the equation of a parabola is \\(y = 6(x - 2)^2 - 8\\).
what is the standard form of the equation?

a. \\(y = 12x^2 - 6x + 8\\)
b. \\(y = 6x^2 - 24x + 16\\)
c. \\(y = 12x^2 - 12x + 16\\)
d. \\(y = 6x^2 - 4x + 4\\)

Explanation:

Expand the squared binomial

$$ (x - 2)^2 = x^2 - 4x + 4 $$

Distribute the leading coefficient

$$ y = 6(x^2 - 4x + 4) - 8 = 6x^2 - 24x + 24 - 8 $$

Simplify the constant terms

$$ y = 6x^2 - 24x + 16 $$

Answer:

• A. \(y = 12x^2 - 6x + 8\)
• B. \(y = 6x^2 - 24x + 16\) (Correct answer)
• C. \(y = 12x^2 - 12x + 16\)
• D. \(y = 6x^2 - 4x + 4\)