Ex: Determine the Least Possible Degree of a Polynomial From the Graph

This video explains how to determine the least possible degree of a polynomial based upon the graph of the function by analyzing the intercepts and turns of the graph.

[GoldPitbull]

so basically to find minimum degree of poly function is just count how many turns it has and add 1?

[Mehkyluh]

Remember, “n” is the degree and n-1 = # of turning points! look at the graphs see how many turning points there are.

Now say there are 5 turning points. Since we know that n-1 = # of turning points, then n-1 = 5 (We looked at the graph, saw 5 turning points and plugged it into the equation) . NOW we SOLVE FOR “n.”

So 5+1 = n, therefore 5+1 = 6!! (6 being the least possible degree)

If you were to really look at it, the least possible degree is just the # of turning points plus 1.

[ccanyouguesswhoiam]

In what world is 3-1=4? What the fuck?!?!?!?!?!

[sailbyzantium]

Thank you!--the number of turns really clarified things--working through a pre-calc workbook where all you have is the graph w/o indication of how many powers the equation is.

In addition to the number of intercepts and turns, would the directions of the graph might matter too: both ends in the same direction = even (graph confirms to some kind of U shape, up or down); each end goes in opposite directions = odd (graph confirms to some kind of S shape, forward or backward).

Have a graph in the workbook that is S-shaped, so odd. It has three turns--but the last doesn't immediately pass through the x-axis, but runs along it for a very short bit, then turns (heads down, then runs along to the right for a tiny bit; than heads down again). As it doesn't go straight through my equation can't be a power of 3, so maybe the next higher odd number? So, 5?

Or would that be FOUR turns total, the last turn actually two: turning first to run along the x-axis (down then right), then turning again to move away from it (right then down)?. So, 4 turns, so a power of 5? This last sounds like a better way, per your explanation--but some of turns sure can be subtle . . . Thanks again!

[beebless]

Some are asking, "n" represents the # of degrees as the exponent. Accordingly to the writing in red to determine the turns, we say "n-1". What does this mean? If we have an exponential degree of 3. The # of terms at MOST would be n-1 or 3-1=2 turns.

[VuMaiHuy]

Very simple, straight forward and absolutely helpful. Thank you.

[thinhtonguyen]

So what does x-intercept do the degree? I see people talk about x-intercept in a lot of video like this but they just kinda ignore it

[whiplash_]

how the hell does 2-1=3 XD. this doesnt make any sense lol

[AlexRodriguez]

Thank you very much, really helped me catch up after being sick.

[whoplays]

but what happens if the curve continues past the negative y axis?

[rose]

Thank you! That was really very useful

[Flavor]

you my friend are a godly man thank you

[Mr.Boyo]

🙏 thank you so much for explaining it so simply 😂
I don’t know what id do without yiu

[syntichekabeya]

Guys : simple, count how many curves a graph has then add 1 and there you have the degree

[ugen]

Thank you so much!

May God bless you!

[eddyj]

Thank you for the clarification, sir!

[tobyque]

My math teacher is bullshit whereas you are great!!!