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The roots of a function, also known as zeros, are the values of the variable for which the function equals zero. In other words, they are the x-values where the function crosses the x-axis on a graph. To find the roots, we set the function equal to zero and solve for the variable.

For the given function, \(y = -(x - 4)(x + 5)\), we identify that the function is a product of two factors. By setting \(y = 0\), we align with finding the points where the graph intersects the x-axis. As seen in the step by step solution, setting the equation to zero and solving for \(x\), we find the roots to be \(x = 4\) and \(x = -5\). This indicates that the function will intercept the x-axis at these points. It's important to understand that roots are critical in understanding the behavior of the function and are used in various fields, such as physics and engineering, for optimal problem solving.

Factoring is a critical algebraic process used to break down equations into simpler components. When it comes to quadratic equations like \(y = ax^2 + bx + c\), factoring can simplify finding the roots of the function. Quadratic equations are often factored into a product of binomials.

In our exercise, the quadratic equation is already in factored form: \(y = -(x - 4)(x + 5)\). To factor a quadratic equation that is not in this form, we look for two numbers that multiply to \(ac\) (the product of the coefficient of \(x^2\) and the constant term) and add to \(b\) (the coefficient of \(x\)). Once these numbers are found, we rewrite the middle term and factor by grouping. Factoring is a powerful tool that simplifies not only finding roots but also analyzing and solving equations for various applications.

Analyzing the graphs of functions allows us to understand their behavior visually. When we graph a function like \(y = -(x - 4)(x + 5)\), we can observe several features such as the intercepts, the vertex, and the direction of opening for a parabola. The x-intercepts correspond to the roots of the function and identify where the graph crosses the x-axis.

As per our given function, the x-intercepts at 4 and -5 tell us that the function will touch the x-axis at these points, often resulting in a change in direction of the graph. This concept is crucial as it lays the groundwork for understanding more complex behaviors of functions, such as end behavior, concavity, and symmetry. Remember, the intercepts are just the starting point; the entirety of the graph gives a comprehensive picture of the function's performance across different domains.