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.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- France: grade 10
- Germany: grade 9
- Syria: grade 10
- Palestine: grade 9
- Ukraine: grade 8
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.