y=x^2+6x+k intersects y=-x^2-6x-k at just one point. Find k
Did you notice one parabola opens up, the other one down
To have only one point of intersection, they must have a common tangent, that is
the slope of one equals the slope of the other
for the 1st: dy/dx = 2x+6
for the 2nd dy/dx = -2x - 6
2x + 16 = -2x -6
4x = 12
x = 3
when x = 3
9 + 18 + k = -9 - 18 - k
2k = 54
k = 27