William Curry

2021-12-24

How to find the end behavior of a quadratic function?

Donald Cheek

Expert

A polynomial function's final behavior is represented by the way its graph behaves $f\left(x\right)$ as $x$ approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers. This means that the sign of the leading coefficient is sufficient to predict the end behavior of the function.

porschomcl

Expert

Quadratic functions have graphs called parabolas.
If graph has both "ends" pointing upward, we would describe this as heading toward infinity. The lead coefficient is a positive number, which causes the parabola to open upward.
If both ends of the function point downward to negative infinity, the lead coefficient is negative.
When you see a quadratic function with lead coefficient positive, you can predict its end behavior as both ends up.

karton

Expert