math
posted by Emily on .
find a function y=ax^2+bx+c whose graph has an xintercept of 1, a yintercept of 2, and a tangent line with slope 1 at the yintercept.

The three given conditions are:
1. For xintercept of 1:
f(x)=y= (x1)(axc) = ax²(c+1)+c
2. For yintercept of 2:
c=2
3. for tangent=1 at y=0
Now find
f'(x)=2ax+b
to satisfy
f'(0)=1, or
2a(0)+b=1
Solve for a, b and c.