Question

If the graph of the following parabola is shifted two units left and three units down, what is the resulting equation?

x=-8y^2

Answer 1

(x+2) = -8(y+3)^2

Explanation:

In this equation, the roles of x and y are different for transformations with a horizontal parabola. (y+3) brings the parabola down 3 instead of up, but on the same side -2 will shift it to the left. So you start with x= -8(y+3)^2 -2 and move the -2 over.

Answer 2

`x=-8\left(y+3\right)^2-2`

Explanation:

Because the x and y have been reversed in this equation, shifting the parabola to the left will be outside of the exponent and shifting up and down will be inside with the exponent.

The equation becomes
`x=-8\left(y+3\right)^2-2`.

Where subtracting by 2 moves it two units to the left and adding by 3 moves it 3 units down.