Question

What does the line y = 5 represent in x=8(y-5)^2+2?
vertex, focus, axis of symmetry, directrix

Answer 1

This is a quadratic equation in its standard form. y = (x-h)^2 + k. In this case, since y and x are exchanged, the vertex is not (h, k), but instead it's (k, h). This also hints that the line y = 5 lies on the vertex of this equation. Plug the numbers in, and you should get (2, 5).

Answer 2

so its the vertex?

Answer 3

is y always y=? always vertex?

Answer 4

Look at the standard form of the quadratic equation again. y = (x-h)^2 + k. The vertex for this equation would be (h, k).

However, your equation has the x and y coordinates swapped. This would yield x = (y-h)^2 + k. In this case, you'll have to swap the coordinates of the vertex, which would become (k, h).

Answer 5

so y is the vertex yes or no