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)