Finding the intercepts in polynomial functions can be simpler than it seems! Here are some easy steps that helped me understand it better:

1. Finding the $y$-Intercept: This is usually the easiest part. To find it, just put $0$ in place of $x$ in the function. The result will give you the point $(0, f(0))$.

   For example, if your function is $f(x) = x^2 - 4$, you would do $f(0) = -4$. So, the $y$-intercept is $(0, -4)$.

2. Finding the $x$-Intercepts: For this, set the function equal to $0$ and solve for $x$.

   You might need to factor, use the quadratic formula, or even graph the function if it's complicated.

   For example, to find the $x$-intercepts of $f(x) = x^2 - 4$, you set $x^2 - 4 = 0$ and factor it like this: $(x - 2)(x + 2) = 0$.

   So, the intercepts are $x = 2$ and $x = -2$.

3. Using Graphing Tools: Sometimes, using graphing calculators or software can really help you see where the intercepts are, especially with more complicated functions.

4. Looking for Symmetry: Even functions (like $x^2$) have $y$-intercepts that are easy to find because they look the same on both sides. Odd functions (like $x^3$) will have the origin (0,0) as one of their intercepts.

With a bit of practice using these methods, you’ll start to feel more confident in finding intercepts in no time!