Question 422630


A parabola is symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at a point called the vertex of the parabola.

You know that two points determine a line. This means that if you are given any two points in the plane, then there is one and only one line that contains both points. A similar statement can be made about points and quadratic functions.

Given three points in the plane that have different first coordinates and do not lie on a line, there is exactly one quadratic function f whose graph contains all three points and  it is a parabola that goes through all three. 

The {{{zeroes}}} would be {{{equidistant}}} on either side of the axis of symmetry at the points where the parabola crosses the {{{x-axis}}}.