The vertex of a parabola is simply where the function is a maximum or a minimum. In the equation given, we'll look at the right side.
Since the #x+3# term is squared, the minimum value of it is #0# (since any squared number is either positive or #0#). Thus, when is #(x+3)^2=0#?
#(x+3)^2=0#
#x+3=0# or #-(x+3)=0#
#x = -3 or x = -3#
#x = -3#
Thus, the vertex is at #x=-3#
We can plug this into the original equation to get #y=5# so the point of the vertex is #(-3,5)#
Now, we can plug in other values of #x# to get different points on the parabola. Some of which could be:
#x=0#, so #y=1/2# and the point is #(0,1/2)#
#x=-1#, so #y=3# and the point is #(-1,3)#
#x=-5#, so #y=3# and the point is #(-5,3)#
Then again, you can choose any #x#-values and get points on the parabola.
