Parabola through three points

Set up and solve a system of three linear equations for a, b, c and check the parabola on its graph.

Guide

A parabola y = a x² + b x + c has three unknowns. Each point on it gives one equation, so three points give a system of three linear equations.

Solve it by the Additionsverfahren in two steps: first eliminate one unknown from two pairs of equations, then solve the system of two equations. Finish with a Probe.

Applications: a throwing arc or a bridge arch measured at three places.