You can put this solution on YOUR website! 3+2x-x^2=0 (editing to make it an equation rather than an expression)
x can be anything, all reals. There are no constraints.
If x is large and positive, y will be very negative.
If x is large and negative, squaring it will make it positive and make y very negative.
If x=0, y=3.
If x=1, Y=4
if x=2, y=3
Vertex is -b/2a= -2/-2. That is x=1
Therefore the maximum is 4.
Range is (-oo, 4]