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

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.

Explanation:

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

Answer 2

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

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