ok, other things that might help you:
we already covered that the local max is at (0, 6) and that is of course the y-intercept. The x-intercept is irrational (the x value for which the function equals "0") but it is approximately (-3/2, 0). We already described the end behaviors. The only last thing to say is squarely in the realm of calculus where the graph is "concave down" between x = negative infinity to 2/3 and it is "concave up" between x = 2/3 to positive infinity. "concave up" means that the graph looks like a "bowl" right-side up in that interval. "Concave down" is an inverted bowl. Hope this all helps. When I learned calculus a thousand years ago, this was the extent of everything we needed to know to graph, and we were able to graph these functions by hand with no computer, so since you are in algebra or algebra II, this really should be all you need I would think.