1. Let's start by understanding what a polynomial is. A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents of variables. 2. To graph a polynomial, we first identify its degree, leading coefficient, and roots (x-intercepts). 3. The general form of a polynomial is $$f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0$$ where $n$ is the degree and $a_n$ is the leading coefficient. 4. Important rules: - The degree determines the shape and number of turning points. - The sign of the leading coefficient affects the end behavior. - Roots are where the polynomial crosses or touches the x-axis. 5. To graph, find the roots by solving $f(x) = 0$, determine the y-intercept by evaluating $f(0)$, and analyze the end behavior based on degree and leading coefficient. 6. Plot these points and sketch the curve smoothly through them, noting the turning points and intercepts. This process helps you visualize any polynomial function clearly.