Find the function y=ax^2+bx+c whose graph contains the points (1,4), (-2,-13), and (2,3)

Question

What is the function y=

If you can tell me how to do it on a ti83, even better!

Answer 1

Use the 3 given points to set up a system of 3 linear equations in 3 unknowns a, b, and c.

a(1)² + b(1) + c = 4

a(-2)² + b(-2) + c = -13

a(2)² + b(2) + c = 3

The system to solve is:

a + b + c = 4

4a - 2b + c = -13

4a + 2b + c = 3

Solve for a, b, and c using elimination, matrix methods, or Cramer's rule.