Question

question 7 of 10

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

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

Explanation:

Set up the vertex form of a horizontal parabola

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

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

Substitute the given point to solve for the coefficient

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

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

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

$$ a = -5 $$

Answer:

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