Checkpoint: Sketching Multiplicities Solution

Sketch the roots. Then write the equation.

a > 0

x = –2, multiplicity 2 (bounce)

x = 0.5, multiplicity 1 (cross-through)

x = 3, multiplicity 3 (snake)

n = 2 + 1 + 3 = 6

$a {(x + 2)}^{2} (x - 0.5) {(x - 3)}^{3} = 0$

Note

Remember to check the degree and end behavior against the value of “a” and the degree of your equation.

Q: Why does the variable a need to be included in your answer when written as the product of factors from a graph?

A: The variable “a” is needed to represent the leading coefficient which determines the end behavior.