determine if the graph cross or touch the x axis to turn around 5(x-5)(x-2)^3

y  =  (x - 5)(x - 2)³

If the factor has an odd power, it will pass through that point; therefore the equation passes through the points  x = 5  and  x = 2.  

The graph will go directly through the point if the power is 1, it "wiggles through" if the power is 3, 5, 7 etc.

If the power is an even number, it touches that point and bounces back to the direction from which it came.

Here's a graph:

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