# How do you find the equation of a parabola given the coordinates of the vertex: (2,3) point : (-1,6)?

##### 2 Answers

Assuming the axis of symmetry is vertical

then the axis of symmetry is

and since

then so is

The general form of the equation for a parabola (with a vertical axis of symmetry) is

We can substitute our three points that we know into this general form:

and solve for

obtaining

So the equation is

Note if the axis of symmetry is horizontal, a similar method can be used; but if the axis of symmetry is other than vertical or horizontal there is insufficient information to derive the parabolic equation.

Assuming that it is a vertical parabola, the equation looks like:

So this parabola has equation:

y=a(x-2)^2+3#

Knowing that

The desired equation is:

If the parabola is horizontal, the answer is different.