Given points (x1, y1), (x2, y2) and (x3, y3), three quadratic functions of the form ax2 + bx + c = y can be formed:
In short, the process of obtaining a quadratic equation from its three given points involves three steps:
- y1 = a(x1)2 + b(x1) + c
- y2 = a(x2)2 + b(x2) + c
- y3 = a(x33)2 + b(x3) + c
- 1 = a(1)2 + b(1) + c
- 1 = a(-2)2 + b(-2) + c
- -1 = a(-1)2 + b(-1) + c
- a = 1
- b = 1
- c = -1
In short, the process of obtaining a quadratic equation from its three given points involves three steps:
- Form three equations (one equation from each point) form ax2 + bx + c = 0
- Solve the three equations simultaneously to get the values of a, b and c
- Put the values of a, b and c in the equation ax2 + bx + c = 0 to obtain the quadratic equation