Question

question 6 of 10

the vertex of this parabola is at (5, 5). when the \\(x\\)-value is 6, the \\(y\\)-value is -1. what is the coefficient of the squared expression in the parabolas equation?

a. 6
b. -6
c. 4
d. -4

Explanation:

Set up the vertex form of the parabola

$$ y = a(x - h)^2 + k $$

$$ (h, k) = (5, 5) \implies y = a(x - 5)^2 + 5 $$

Substitute the given point to solve for the coefficient

$$ (x, y) = (6, -1) $$

$$ -1 = a(6 - 5)^2 + 5 $$

$$ -1 = a(1)^2 + 5 $$

$$ a = -6 $$

Answer:

• (A) 6
• (B) -6 (Correct answer)
• (C) 4
• (D) -4