Three Points Parabola Calculator

Overview & Instructions

This calculator finds the standard equation of a parabola with a vertical axis (\( y = ax^2 + bx + c \)) given any three points on its graph.

The logic is based on solving a system of three linear equations with three variables as outlined in our step-by-step solver: Find Equation of Parabola Passing Through three Points.

How to Use:

1. Enter the \(x\) and \(y\) coordinates of the three points A, B, and C.
2. Inputs can be integers, decimals (e.g., 1.02), or fractions (e.g., 4/5).
3. Choose the number of decimal places for the approximated output.
4. Click "Calculate" to view the exact fractional equation and the decimal approximation.

Note: If at least two points lie on the same vertical line (i.e., they share the same \(x\)-coordinate), no vertical parabola can pass through all three points.