Question

the vertex of the parabola below is at the point (-4, -2). which of the equations below could be the one for this parabola?

a. \\(x = 2(y - 4)^2 - 2\\)
b. \\(x = -2(y + 2)^2 - 4\\)
c. \\(x = 2(y + 2)^2 + 4\\)

Explanation:

Identify the orientation and vertex of the parabola

Using the Vertex Form of a Parabola knowledge point

$$
LATEXBLOCK0
$$

Substitute the vertex coordinates into the standard form

Using the Parabola Equation knowledge point

$$
LATEXBLOCK1
$$

Determine the sign of the coefficient

Using the Parabola Equation knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) \(x = 2(y - 4)^2 - 2\)
• (B) \(x = -2(y + 2)^2 - 4\) (Correct answer)
• (C) \(x = 2(y + 2)^2 + 4\)