Question

question 4 of 10

the vertex of this parabola is at \\((2, -4)\\). when the \\(x\\)-value is 3, the \\(y\\)-value is -1. what is the coefficient of the squared expression in the parabolas equation?

a. 5
b. 3
c. -2
d. 1

Explanation:

Write the vertex form of the parabola

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

$$ (h, k) = (2, -4) \implies y = a(x - 2)^2 - 4 $$

Substitute the given point to solve for the coefficient

$$ (x, y) = (3, -1) $$

$$ -1 = a(3 - 2)^2 - 4 $$

$$ -1 = a(1)^2 - 4 $$

$$ a = 3 $$

Answer:

• (A) 5
• (B) 3 (Correct answer)
• (C) -2
• (D) 1