Write a Quadratic Equation Given Two Points Calculator

Writing a quadratic equation given two points is a fundamental concept in algebra. It’s crucial for understanding the relationship between points and equations, and it’s widely used in various fields, including physics, engineering, and data analysis.

How to Use This Calculator

Enter the coordinates of the first point (x1, y1) in the respective input fields.
Enter the coordinates of the second point (x2, y2) in the respective input fields.
Click the “Calculate” button.

Formula & Methodology

The quadratic equation can be found using the following formula:

y = ax² + bx + c

Where ‘a’, ‘b’, and ‘c’ are coefficients calculated as follows:

a = (y2 – y1) / (x2 – x1)
b = -(2 * a * x1) + (y1 + y2) / (x2 – x1)
c = (x1 * y2 – x2 * y1) / (x2 – x1)

Real-World Examples

Data & Statistics

Comparison of Quadratic Equations for Different Points
Point 1 (x1, y1)	Point 2 (x2, y2)	Quadratic Equation
(1, 2)	(3, 6)	y = 1.5x² – 0.5x + 2
(2, 3)	(4, 7)	y = 1.25x² – 2.5x + 3

Expert Tips

Always ensure the points are not on the same horizontal line (x-coordinate) to avoid division by zero.
For a more accurate result, use points that are far apart.

To find the vertex of the parabola, use the formula: x = -b / (2a).
To find the y-coordinate of the vertex, substitute the x-value from step 1 into the quadratic equation.

Interactive FAQ

What if the points are on the same horizontal line?

If the points are on the same horizontal line, it’s not possible to find a unique quadratic equation as there are infinitely many equations that pass through two points on the same line.