Find an equation of the parabola in standard form passing through the points: (-2, 9), (-4, 5), (1, 0)

Answer 1

2 possibilities for a standard parabola, vertical or horizontal

either it's of the form y=ax^2 + bx + c, a downward opening parabola with a<0

or it's x = ay^2 + bx + c with a>0

either one collapses to y = a(x-h)^2 + k

or to x = a(y-k) + h

plug in the 3 points separately to get a series of equations

Either you get one parabola, two parabolas possible, or none.

If none there still could be non-vertical, non-horizontal parabolas, but they would have an xy term, which is quadratic, but not the usual x^2 or y^2