EQUATRAN Logo
EQUATRAN Logo

Quadratic Equation through 3 Points

Category: Mathematics

Demonstrates: Linear simultaneous equations; Array variables

Problem Description

Given the x, y co-ordinates of three points, obtain a quadratic simultaneous equation that passes through these points.

Assuming the co-ordinates of three points to be (x1, y1), (x2, y2) and (x3, y3), the following equations can be formed:

ax12+bx1+c=y1
ax22+bx2+c=y2
ax32+bx3+c=y3

The EQUATRAN source text for this problem is:

/*  Quadratic equation defined by three points  */

VAR x(3), y(3)
y = a*x^2 + b*x + c
INPUT x, y
OUTPUT a, b, c

Enter the lines above into a new source text window, then click the Run button:

Input values are now requested, type 1, 5, 9 and click Input to enter the values for X, then repeat for the Y values 6, 3, 10. Click Go.

Input

The calculation result is displayed:

/*  Quadratic equation defined by three points  */                      

<<   input data   >>
x               =                
  1) 1                2) 5                3) 9             
y               =                
  1) 6                2) 3                3) 10            

<<   results   >>
a               =  0.3125        
b               =  -2.625        
c               =  8.3125        

The EQUATRAN file for this example can be downloaded from the link below:

Download example