Question

the standard form of the equation of a parabola is (y = 5x^2 + 20x + 14).
what is the vertex form of the equation?

a. (y = 5(x + 2)^2 + 10)
b. (y = 5(x + 2)^2 - 6)
c. (y = 5(x + 4)^2 + 10)
d. (y = 5(x + 4)^2 - 6)

Explanation:

Factor the leading coefficient from the variable terms

$$ y = 5(x^2 + 4x) + 14 $$

Complete the square inside the parentheses

$$
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$$

Simplify to vertex form

$$ y = 5(x + 2)^2 - 6 $$

Answer:

• A. \(y = 5(x + 2)^2 + 10\)
• B. \(y = 5(x + 2)^2 - 6\) (Correct answer)
• C. \(y = 5(x + 4)^2 + 10\)
• D. \(y = 5(x + 4)^2 - 6\)