Graphing polynomial functions is a great way to see where their zeros (or roots) are. These zeros are the points where the graph meets the x-axis.

Why Are Zeros Important?

• Solutions to Equations: Zeros tell us where the equation $f(x) = 0$ is true.
• Real-world Contexts: They can show important moments, like when a business is making the most money or losing the least.

Example

Let’s look at the quadratic function $f(x) = x^2 - 4$. When we graph this function, we see it crosses the x-axis at $x = -2$ and $x = 2$. These points show us the zeros of the function.

By marking these points on the graph, we can clearly see where the function switches from positive (above the x-axis) to negative (below the x-axis).

Graphing helps us understand these ideas better. It turns complicated concepts into something we can see and grasp more easily.