Find values of a and b...

I'm really having trouble with these two problems in my homework... I'm just not sure where to start and would appreciate a push in the right direction.

In my class, we've just gotten through the quotient rule for derivatives.

1. Find values of a and b so that y = ax^2 + bx has a tangent line at (1,1) whose equation is y = 3x - 2

This is what I did, but my answer did not check out when I graphed it and such:

a(1)^2 + b(1) = 3(1) - 2 <---This is a guess, can I do this?

So...

a + b = 1 or b = 1-a or a = 1-b

y' = 2ax + b =3 <---since the slope of the tangent line is 3, at (1,1)

2a(1) + b = 3

So...

2a + b = 3

2a + (1-a) = 3

a = 4

2(1-b) + b = 3

2-b = 3

b = -1

But when I graphed both, the equation of the tangent line didn't lie on (1,1) of the graph y = 4x^2 - x. Where did I go wrong?

**2. Find the equation of the line(s) that are tangent to the graphs of y=x^2 and y= -x^2 +6x - 5.**

And I don't know where to start for this one...