Question

There is a unique parabola whose symmetry axis is parallel to the y-axis, and that passes through the three points (1, 1), (−2, −2), and (0, −4). Write an equation for it. Given any three points, must there be a parabola that will pass through them? Explain

Answer 1

The equation for the parabola is y = -1/2x^2 + 3. No, there must not be a parabola that will pass through three points; it could also be an ellipse or hyperbola depending on how those three points are arranged in space.