A friend of mine has a few problems with his math. It's been quite a while since he has done it, and right now he is expected to simply know it all. Therefore, I will post this question on his behalf. I've tried to help him, but I'm not yet this far along with math at school.
$$f(x) = x^2 +10x = -20 + k$$
We started off with $f(x) = 0,5(x+3)^2 + 1$ and $g(x) = 2x + k$. The question is for what $k\in \mathbb R$ does $g(x)$ through the parabola $f(x)$. If somebody could provide us with at least a strategy on how to solve this, my friend and I would be very thankful.
Thanks in advance.