The vertex form of a quadratic equation is expressed as
#y=a(x-h)^2+k#
Where #(h,k)# is the vertex. That vertex is a maximum if the coefficient of #x^2# term is negative. But the vertex is a minimum if the coefficient of the #x^2# term is positive.
For the equation we are given, we can easily add zeros to put it into vertex form
#y=5x^2# becomes
#y=5(x-0)^2+0#
This quadratic equation has a vertex at #(0,0)# and, because the coefficient #5# of the #x^2# term is positive, we know this vertex is a minimum.
The #y#-intercept occurs when #x=0#, which is again the origin at #(0,0)#. The #x#-intercept occurs when #y=0#, which can only happen when #x=0#. So the only #x# or #y# intercept happens at the vertex, all of which converge at the origin: #(0,0)#.
The graph is as follows:
graph{5x^2[-2,2,-1.5,10]}
