Suppose that f(x) is a quadratic function such that f(1)=4, f(2)=13, and f(0)=-1. Find the general form for f(x).

Answer 1

f(x) = ax^2 + bx + c
0a+0b+c = -1
a+b+c = 4
4a+2b+c = 13
now solve as usual.

Answer 2

y = a x^2 + b x + c
4 = a + b + c
13 = 4 a + 2 b + c
-1 = 0 + 0 + c
=============== so c =-1
5 = a + b
13 = 4 a + 2 b
===========
10 = 2 a + 2 b
13 = 4 a + 2 b
------------------- subtract
-3 = -2 a
a = 3/2
3/2 + b = 10/2
b = 7/2
so
y = 3/2 x^2 + 7/2 x - 1
or
2 y = 3 x^2 + 7 x - 2