How do you find the end behavior of a quadratic function?

1 Answer
Sep 13, 2014

Quadratic functions have graphs called parabolas. my screenshot 1 my screenshot 2

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:
my screenshot3

Its end behavior:
as #x->\infty, y->-\infty# and as #x->-\infty, y->-\infty#
(right end down, left end down)