Finding a and b, of ax^2 + bx + c, when given an equation of the tangent line

Hey!

I didn't really know what to put as a title so I hope it describes the problem relatively well... I have been working on this problem for about 20 minutes and haven't come very far, so I was hoping for someones help in putting me in the right direction!

**Question**

For what values of a and b is the line tangent to the parabola when x = 2?

** Solution **

I feel I have all the pieces of the puzzle, but there is some trick to putting it together.

I know how to find the equation of a tangent line when given an equation and a point on that equation (just find the derivative and then use y = mx + b and sub in everything to find b). However in this question I don't even know where to start. I know that .

If I sub 2 into either y' or y I get y = 4a(or y' = 4a). How do I use this information to solve for a and b?

This feels like an easy problem that I just can't wrap my head around!

Thanks for your help!