Consider the equation 0 = x^2 + 4x + 4. We can solve this by factoring as a perfect square trinomial, so 0 = (x+ 2)^2-> x = -2 and -2. Hence, there will be two identical solutions.
The discriminant of the quadratic equation (b^2 - 4ac) can be used to determine the number and the type of solutions. Since a quadratic equations roots are in fact its x intercepts, and a perfect square trinomial will have 2 equal, or 1 distinct solution, the vertex lies on the x axis. We can set the discriminant to 0 and solve:
k^2 - (4 xx 1 xx 36) = 0
k^2 - 144 = 0
(k + 12)(k - 12) = 0
k = +-12
So, k can either be 12 or -12.
Hopefully this helps!
