The equation for a parabola has the form y=ax2+bx+c, where a, b, and c are constants and a≠0. find an equation for the parabola that passes through the points (−1,−9), (1,7), and (−6,−14).

The equation of parabola is

For point (-1,-9), equation of parabola is

For point (1,7), equation of parabola is

For point (-6,-14), equation of parabola is

So we have three equations , which are

Subtracting first two equation will give

Subtracting second and third equation gives

Substituting 8 for b, we will get

back substituting 8 for b and 1 for a, we will get

So we have

Therefore required equation is