Question

Explain how you can determine if four points lie on a single parabola

Answer 1

1.) Plug them into the equation

2.) They should all be symmetric to some line. If this is a slant asymptote, it's much harder to determine. However, if you are being asked this question, I would guess you're taking either Algebra I or II. In which case there should be a vertical or horizontal line they are symmetric to... and there should be 2 sets of points with equivalent X OR Y values.... determine the line. If you're able to, they're on a parabola....if not, they probably aren't.

Answer 2

four points in the plane determine two conjugate parabolas, each of which ... system we can fit a second degree polynomial to the three points P1,P3,P4. ... of the quadratic give the two orientations in which the four points lie on a single ... shows that if a parabola with vertical axis intersects a horizontal line at points P,Q