Question

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

Answer 1

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)