For $x$ and $k$ real numbers, determine the values of $k$ for which the graphs of $f(x)=x^2-4$ and $g(x)=2|x|+k$ do not intersect For $x$ and $k$ real numbers, determine the values of $k$ for which the graphs of $f(x)=x^2-4$ and $g(x)=2|x|+k$ do not intersect.
For $x$ and $k$ real numbers, determine the values of $k$ for which the graphs of $f(x)=x^2-4$ and $g(x)=2|x|+k$ have exactly 2 intersections.
I graphed them on Desmos and found that when k is smaller than -5 they don’t have any intersections and when k is greater or equal to -5 they’ll have two intersections, but I really have no idea what to begin with when it comes to handwriting.

Set the following equations from $f(x)=g(x)$, 
$$ x^2 -4 = 2x+k$$
$$ x^2 -4 =- 2x+k$$
Or, 
$$ x^2 -2x -(4+k)= 0$$
$$ x^2 +2x -(4+k)= 0$$
Their discriminant is
$$\Delta =b^2-4ac = 20+4k$$
If they do not intersect, meaning above equations have no solution, we set $\Delta <0$. So, $k <-5$.
If they have two intersections, meaning above equations have one solution each, we set $\Delta =0$. So, $k=-5$
