Answer:
(3,0) the graph touches the x-axis
Step-by-step explanation:
the graph of [tex]y = (x + 2)(x + 1)(x – 3)^2[/tex]
we need to check what happens to the graph near the point (3,0)
In f(x) we have (x-3)^2
LEts plug in 3 for x and check
[tex]y = (3 + 2)(3 + 1)(3 – 3)^2[/tex]
y=0, so (3,0) is one of the zero of the given f(x)
In f(x) we have [tex](x-3)^2[/tex]
Exponent is 2 that is even. It means the multiplicity is even.
When the multiplicity is even then the graph touches the x axis but does not cross x axis
So at (3,0) the graph touches the x-axis
