Another application of linear systems is fitting curves to given data. For example, consider the polynomial of degree at most two given by f(x) = ax2 + bx + c. There are three coefficients and hence we can attempt to specify three conditions on f to determine a unique polynomial. Set up and solve a linear system to find a function f(x) = ax2 + bx + c that satisfies the conditions below. f(0) = 3, f(1) = 4, f(2) = 7 Solution since, f(x) = ax 2 + bx + c f(0) =3 implies c=3 (putting x= 0) f(1) = 4 implies a + b + c = 4 or a + b = 1 f(2) = 7 implies    4a + 2b + c =7 or 4a + 2b=3 Solving the above two equations we get a= b= 0.5 therefore the required f(x) = (x 2 + x + 6)/2 .

1. Another application of linear systems is fitting curves to given data. For example, consider the
polynomial of degree at most two given by f(x) = ax2 + bx + c. There are three coefficients and
hence we can attempt to specify three conditions on f to determine a unique polynomial. Set up
and solve a linear system to find a function f(x) = ax2 + bx + c that satisfies the conditions
below. f(0) = 3, f(1) = 4, f(2) = 7
Solution
since, f(x) = ax 2
+ bx + c
f(0) =3 implies c=3 (putting x= 0)
f(1) = 4 implies a + b + c = 4 or a + b = 1
f(2) = 7 implies   4a + 2b + c =7 or 4a + 2b=3
Solving the above two equations we get a= b= 0.5
therefore the required f(x) = (x 2
+ x + 6)/2