Incorporating Multiplicity (Cross vs. Tangent/Bounce)
Create a polynomial P(x) that has a zero at x = -1 where the graph crosses the axis, and a zero at x = 2 where the graph is tangent to (bounces off) the axis.
Now graph your polynomial below to verify.
What change did you make to the exponent or factor of (x - 2) to make the graph bounce instead of cross?
Looking at your equation, how would a classmate know which zero is a 'cross' and which is a 'bounce' without looking at the graph?
Why does an even exponent (like 2) keep the output values on the same side of the x-axis, while an odd exponent (like 1) causes the values to change sign from positive to negative?