Question

Which equation does the attached graph represent?

A.
`x=-2(y+3)^2-2`
B.
`x=2(y+3)^2-2`
C.
`y=-2(x+3)^2-2`
D.
`y=2(x+3)^2-2`

Answer 1

Hi there!

`\large\boxed{B. \text{ } x = 2(y + 3)^(2) -2}`

The transformation formula of a horizontal-facing parabola is:

x = ±a(b(y - k)) + h, where the vertex is at (h, k).

Looking at the graph, we can see a vertex at (-2, -3) with a stretch of 2. The graph is also pointed towards the RIGHT, which means that the coefficient "a" must be positive. Therefore:

The only logical answer choice is B, or x = 2(y + 3)² - 2.

The formula indicates that:

* Vertex at (-2, -3)

* Stretch of 2

* Right-facing parabola