How do you find the end behavior of a quadratic function?
Quadratic functions have graphs called parabolas.
The first graph of y = ##x^2## has both “ends” of the graph pointing upward. You would describe this as heading toward infinity. The lead coefficient (multiplier on the ##x^2##) is a positive number, which causes the parabola to open upward.
Compare this behavior to that of the second graph, f(x) = ##-x^2##.
Both ends of this function point downward to negative infinity. The lead coefficient is negative this time.
Now, whenever you see a quadratic function with lead coefficient positive, you can predict its end behavior as both ends up. You can write: as ##x->infty, y->infty## to describe the right end, and
as ##x->-infty, y->infty## to describe the left end.
Last example:
Its end behavior:
as ##x->infty, y->-infty## and as ##x->-infty, y->-infty##
(right end down, left end down)