Question

question 1 of 10

the vertex form of the equation of a parabola is (y = 3(x - 4)^2 - 22).
what is the standard form of the equation?

a. (y = 9x^2 - 26)
b. (y = 3x^2 - 24x + 4)
c. (y = 3x^2 - 24x + 26)
d. (y = 3x^2 - 18)

Explanation:

Expand the squared binomial

$$ (x - 4)^2 = x^2 - 8x + 16 $$

Distribute the coefficient

$$ 3(x^2 - 8x + 16) = 3x^2 - 24x + 48 $$

Subtract the constant term

$$ y = 3x^2 - 24x + 48 - 22 = 3x^2 - 24x + 26 $$

Answer:

• A. \(y = 9x^2 - 26\)
• B. \(y = 3x^2 - 24x + 4\)
• C. \(y = 3x^2 - 24x + 26\) (Correct answer)
• D. \(y = 3x^2 - 18\)