Quadratics through 3 Points
David B. Sher
Mat/Stat/CMP Dept
Nassau Community College
 
You can always find a quadratic of the form ax2+bx+c that passes through 3 points. This page will guide you through the process of finding that quadratic. 
First you use your three points to set up 3 equations. 
Enter the three points:
 
 
X
Y
Point 1
Point 2
Point 3
Use the points to construct 3 equations:  (x2 is the coefficient of a and x is the coefficient of b)
  1. A+B+C=
  2. A+B+C=
  3. A+B+C=

    4. Then you subtract the first equation from the third to eliminate C

  4. A+B=

    5.  

    Then you subtract the second equation from the third to eliminate C

  5. A+B=

    6.  

    Now you must divide every number of the fourth equation by its B coefficient. 

  6. A+B=

    7.  

    Now you must divide every number of the fifth equation by its B coefficient. 

  7. A+B=

    8.  

    Now subtract equation 7 from equation 6 and solve for A

  8. A = 

    9. After plugging the value of A into equation 7 we get this equation:

  9. +B=

    10. Now solve for B

  10. B = 

    11. After plugging the values of A and B into equation 1 we get this equation:

  11. *

    12. +*
    +C=

    Now solve for C

  12. C = 

Congratulations, the function you have found is:

Y=x2+x+
You can check the result from this equation in this table:
X
Entered Y
Quadratic's Y

Copyright © David B. Sher 1997