Determine the quadratic if f(-1)=4, f(1)=2, f(2)=7 .

Let the function be f(x) = ax^2 + bx +
c

Given the points ( -1, 4) , (1, 2), and ( 2,7) are on the
curve f(x).

Let us substitute
:

==> f(-1) = a(-1)^2 + b(-1) + C =
4

==> a - b + c =
4.................(1).

==> f(1) = a(1^2) +b(1) + C =
2

==> a + b + c =
2...............(2).

==> f(2) = a(2^2) + b(2) + C =
7

==> 4a + 2b + C =
7.............(3).

Now we have a system of 3 equations and
3 variables.

We will use the elimination method to
solve.

Let us add (1) and
(2).

==> 2a+ 2c =
6

==> a + C = 3
...............(4).

Now we will add 2*(1) and
(3)

==> 2a-2b + 2c =
8

==> 4a+2b + C =
7

==> 6a + 3c =
15

==> 2a + c =
5............(5)

Now subtract (4) from
(5).

==> a =
2

==> c = 1

==>
b = -1

==> f(x) = 2x^2-x +
1