Polynomial graphs: FAQ

The zeros of a polynomial are the x-values where the polynomial crosses the x-axis. In other words, they're the points where the polynomial equals $0$0.

Polynomials can be positive or negative in certain intervals. For example, a polynomial might be positive for all $x$x-values less than $-2$minus, 2, negative between $-2$minus, 2 and $3$3, and positive again for all $x$x-values greater than $3$3.

The end behavior of a polynomial tells you what the polynomial "looks like" as it approaches positive and negative infinity. For example, if a polynomial "increases without bound" as $x$x approaches positive infinity, it means the polynomial keeps getting higher and higher on the graph the further to the right you go.

Polynomials are used in a variety of real-world applications, from engineering to economics. For example, in physics, polynomials can be used to model the trajectory of an object in motion. Understanding the zeros, positive and negative intervals, and end behavior of a polynomial can help us understand the shape of the graph and make predictions about the system it models.