Question

If the graph of the following parabola is shifted one unit left and two units up, what is the resulting equation in vertex form? x^2=12

Answer 1

ANSWER

${(x + 1)}^{2} =12(y - 2)$

EXPLANATION

The original parabola has equation

${x}^{2} = 12y$

This parabola has its vertex at the origin:

If the parabola is shifted one unit left and two units up, then its new vertex is at (-1,2).

The equation of the new parabola is now of the form:

${(x - h)}^{2} =1 2(y - k)$

where (h,k) is the vertex.

Substitute the vertex to get:

${(x - - 1)}^{2} =12(y - 2)$

${(x + 1)}^{2} =12(y - 2)$