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A graphing calculator is a powerful tool that can help solve polynomial equations. To begin, you need to input the given equation into the graphing calculator. For example, if the problem is to solve the equation \(x^3 - 3x^2 - 198x + 1080 = 0\), you should enter this exact function into the graphing calculator's input interface. Most graphing calculators have a 'Y=' button or a direct function entry method where you can type in your equation. Once you've entered the equation, you're ready to move to the next step of plotting the function. Remember, typing the equation correctly is crucial to ensure accurate results.

Roots of an equation are the values of \(x\) that make the equation equal to zero. In the context of graphing polynomials, the roots are the points where the graph intersects the x-axis. After you have entered your function into the graphing calculator and plotted it, you will look for these intersection points. These points correspond to the x-values where the graph crosses the x-axis \((y = 0)\). For our example, when you plot \(x^3 - 3x^2 - 198x + 1080 = 0\), you might see three such intersections since it is a cubic polynomial (which can have up to three real roots). Accurate identification of these roots requires carefully examining the graph on the calculator's display.

Plotting functions on a graphing calculator helps visualize the behavior of the polynomial equation. Once you’ve inputted the equation \(x^3 - 3x^2 - 198x + 1080\), you can plot the function by pressing the appropriate button (often labeled 'GRAPH') on your graphing calculator. The graph will display a curve that represents all possible solutions to the equation in the coordinate plane. Key points to observe include where the graph intersects the x-axis as these points are the solutions, or roots, of the equation. Additionally, plotting the function helps to understand the polynomial's overall behavior, including any turning points or asymptotic behavior if they exist. Engaging with the visual representation of the function can clarify complex algebraic relationships, making it easier to solve higher-order polynomials.