Question

find a function y=ax^2+bx+c whose graph has an x-intercept of 1, a y-intercept of -2, and a tangent line with slope -1 at the y-intercept.

Answer 1

The three given conditions are:

1. For x-intercept of 1:
f(x)=y= (x-1)(ax-c) = ax²-(c+1)+c
2. For y-intercept 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.