Find the x intercepts and graph

y = (x + 3)^2 (2x + 1) (2 - x)

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The given function is `y = (x + 3)^2 (2x + 1) (2 - x)`

To find x intercepts set `y=0` . So that,

`(x + 3)^2 (2x + 1) (2 - x)=0`

Using zero product property:

`(x + 3)^2=0 rArr x=-3`

`(2x + 1)=0 rArr x=-1/2`

`(2 - x)=0 rArr x=2`

**Therefore, the x intercepts are** `-3, -1/2 and 2.`

The graph of the given function is:

Since, the given function is quartic, the graph shows three turnings intersecting the x-axis at -3, -1/2 and 2.

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