1234
of 4

Multiplicities

Check it out:

Find the real zeros of

f ( x ) = ( x - 3 ) ( x + 2 )^2

then draw a rough sketch of the graph:

What's the basic shape?

f ( x ) = ( x - 3 ) ( x + 2 )^2 ... leading term is x^3 ... the graph will be a basic cubic shape

*Finding the basic shape first will totally save you
if you forget about the kiss thang!

What are the real zeros?

( x - 3 ) ( x + 2 )^2 = 0 gives x - 3 = 0 or ( x + 2 )^2 = 0 which gives x = 3 , x + 2 = 0 which gives x = 3 and x = -2

real zeros: -2 (kiss), 3 (shoot through)

Let the shape guide you...

basic cubic shape

graph of f ( x ) = ( x - 3 ) ( x + 2 )^2