I think that answer is wrong
The tangent to the equation will have an equation in the form y = mx + yin
(where yin= yitnercept, havent called it c as you already have c defined)
therefore tangent equation is y = (2ax+b)x + yin
you also have an equation y = ax^2 + bx + c
you know these intercept so you can equate them, ie.
ax^2 + bx + c = (2ax +b)x + yin
then solve for yin