Posted by **Emily** on Saturday, October 9, 2010 at 11:48pm.

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.

- math -
**MathMate**, Sunday, October 10, 2010 at 9:54am
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.

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