Answer:
k can either be
12
or
−
12
.
Explanation:
Consider the equation
0=x2+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 (b2−4ac) 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:
k2−(4×1×36)=0
k2−144=0
(k+12)(k−12)=0
k=±12