Question

What does the graph of y = (x + 2)(x + 1)(x – 3)2 do near the point (3, 0)?

The graph is the x-axis to its left, then , and is the x-axis to its right.

Answer 1

Answer:

(3,0) the graph touches the x-axis

Step-by-step explanation:

the graph of $y = (x + 2)(x + 1)(x – 3)^2$

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

$y = (3 + 2)(3 + 1)(3 – 3)^2$

y=0, so (3,0) is one of the zero of the given f(x)

In f(x) we have $(x-3)^2$

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

Answer 2

Answer:

I am not completely sure but I think the answer is The graph is  

below  the x-axis to its left, then  is tangent to the x-axis at the point , and is  

above  the x-axis to its right.

Step-by-step explanation:

i graphed it and analyzed it i could be wrong tho.