Which of the following graphs could represent a 5th-degree polynomial function, with 3 distinct zeros, 2 zeros with a multiplicity of 2, and a positive leading coefficient?

Question

shaniehh · Answer

attachment

shaniehh · Answer

@mathmale

mathmale · Answer

"Fifth degree" tells us that the highest x power is 5 (which is odd).  As is true of the function y=x^3, the graph starts in Quadrant III and ends in Quadrant I.  
This fact should immediately help you to eliminate the graphs that could not be correct for this problem.  Label the graphs a, b, c and d.  Which letters represent possible solutions?

shaniehh · Answer

D?

shaniehh · Answer

Is it D? @mathmale

mathmale · Answer

Please explain why you think the correct answer is D.

shaniehh · Answer

because u said the highest x point is 5

mathmale · Answer

Shaniehh, I did not say that.  I used the word "power," not "point."  Big difference.

The fifth power of x is written as x^5, the fourth as x^4, and so on.

mathmale · Answer

So, again, I ask you to explain why you believe D is the correct answer.

shaniehh · Answer

Idk i guess its not

mathmale · Answer

I didn't say that D was incorrect.  I'm pressing you to show that you understand the concepts involved in the problem by explaining why you chose D.

shaniehh · Answer

okay well in D its going from the 3rd Quadrant to the 1st

shaniehh · Answer

I mean C is going from the 3rd Quadrant to the 1st

shaniehh · Answer

B!!my bad

mathmale · Answer

"Fifth degree" tells us that the highest x power is 5 (which is odd).  As is true of the function y=x^3, the graph starts in Quadrant III and ends in Quadrant I.  
This fact should immediately help you to eliminate the graphs that could not be correct for this problem.  Label the graphs a, b, c and d.  Which letters represent possible solutions?

I've looked at all four possible answers and have already eliminated both C and D, because the graph does not both start in QIII and end in QI.

mathmale · Answer

try again.  All you have left to choose from now are A and B.  Explain your choice.

shaniehh · Answer

I ment B

mathmale · Answer

Shaniehh, both you and I would benefit if you'd please explain your choices.  Why, for example, did you choose B over A?  Hint:  What does "a multiplicity of 2" mean, and what effect does that have on the shape of the graph of this 5th order polynomial?

mathmale · Answer

I'd encourage you to look up "multiplicity " as it relates to algebraic functions.

mathmale · Answer

I need to get off the 'Net now.  However, i f you choose to respond to my questions, I'll see them next time I log on again.  Good night.