Using the Even and Odd Powers of Theorem, determin whether the graph of P crosses the x-axis or intersects but does not cross the x-axis.
P(x)=(x+2)^2(x-6)^10

Question

Using the Even and Odd Powers of Theorem, determin whether the graph of P crosses the x-axis or intersects but does not cross the x-axis.
P(x)=(x+2)^2(x-6)^10

anonymous · Answer

value of this funtion will always >or= 0 hence it will touch the x-axis but won't cross it

yttrium · Answer

Any expression that is raised to positive even integer will give you a value of more than or equal to zero. In your case, you have (x+2)^2 and (x-6)^10
Lets consider 1st (x+2)^2, you might think that if you substitute -3 for instance, will lead to (-3+2)^2 which is (-1)^2, still it will arrive at a positive answer.
Same as (x-6)^10, you might think that if we substitute 5, it will become (-1)^10, same as the 1st instance, it will still lead to positive answer.

On the other hand, if we substitute -2 to (x+2)^2 and 6 to (x-6)^10, the answer will be 0.
Hence, our conclusion is that it just intersects but does not cross the x-axis.