How do you find the equation of a parabola given the coordinates of the vertex: (2,3) point : (-1,6)?
Assuming the axis of symmetry is vertical
then the axis of symmetry is
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
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:
The desired equation is:
If the parabola is horizontal, the answer is different.