1) for sliders a-e, there is always an x-intercept at the point (a,b...e, 0)[br]2) the end behavior stays the same regardless of the values chosen for numbers a-e

The graph crosses the x-axis at all of these points (1,0), (2,0), ... , (5,0). This happens because in the equation any time x is one of these values, y = 0, meaning that the numbers 1-5 are roots of the polynomial function.

The graph "bounces" off the x-intercept when a and b = -4 but passes through the x-intercept at all of the other points.

The graph "snakes through" the x-intercept at the value of a, b, and c but passes straight through the x-intercept for the values of d and e.

When no values are in common, the graph passes straight through the roots on the x-axis. When there are an even number of values in common, the graph "bounces" at the root on the x-axis. When there are an odd number of values in common greater than 1, the graph passes through the root but levels out before continuing.