Find the equation of a parabola (quadratic function) from a vertex and a point, or three points.
Coordinate Inputs
Equation Result
y = x²
Standard Form
The unique quadratic equation fitting the points.
Vertex Formy = (x )²
Leading Coeff (a)1.000
Vertex(0.00, 0.00)
About this calculator
Finding Quadratic Equations
A parabola is defined by a quadratic equation. You can find this equation if you know the vertex and one other point, or any three non-collinear points on the curve.
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Pro Tips
Vertex Form (y = a(x-h)² + k) is easiest when you know the vertex.
Standard Form (y = ax² + bx + c) is found by expanding.
Three points require solving a system of 3 linear equations.
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Fun Facts
"Any three non-collinear points define a unique parabola (assuming vertical axis)."
"This process is a form of curve fitting or regression."
