Can someone give me a good simplified explanation on Polynomials in form. I am trying to grasp an understanding of:

Constant Function f(x)=asub0
Linear Function f(x)=asub1x + asub0
Quadratic Function f(x)=asub2xsquared + asub1x + asub0

I am taking a Discrete Structures course and it has been over 15 years since I worked with this stuff.

Sample problem:

Draw a graph of the following polynomial function. Find all the intercepts and note where the functions are increasing and decreasing:

a. f(x)=xsquared -4

b. g(x)=xsquared -2x + 1

If someone knows a good reference that would be good too.

I have read the chapter 3 times and still lost.

 

In your sample you can find intercepts by having both equations equal to each other and add/subtract all the variables to one side. Have the remaining variables equal to the constant. Find the value for x. Now plug in the x value(s) to get your y, g(x), f(x) value.

(x squared)-4 = (x squared) - 2x + 1
(x squared)-(x squared)-4 = (x squared) - 2x + 1 -(x squared)

-4 = -2x + 1
-4 - 1 = -2x + 1 - 1
-5 = -2x
2.5 = x

Now plug the value of x back into one of the original equations to get your g(x) co-ordinate....g(x) = y = 2.25

Where the two equations meet each other is at (2.5, 2.25)

Is any of this coming back?

 

To find where the transition point (the point where a function changes from an increasing to decreasing or vice versa) of each function without graphing each equation is fairly easy also. First take the first equation and set it equal to 0. Now take its first derivative.

(x squared) - 4 = 0
f prime is now 2x - 0 = 0
(2x)(.5) = (0)(.5)
x = 0
Now plug 0 back into the equation to get the y-coordinate
This equation's transitions occurs at (0,-4)

Now do the same for the second equation:

(x squared) - 2x + 1 = 0
f prime is now 2x - 2 + 0 = 0
2x-2 = 0
2x = 2
x = 1

Now plug x back into the original equation and we get y = 0.
This equation's transition occurs at (1,0).


If you need help with how to find how to find whether a function is increasing or decreasing at a given point or range, let me know. . .I can explain that too.

 

Luder94,

Thank you! I think the light has come on finally.

 

Not a problem. . .just for quick explanation before it may come up. To find whether a function is increasing or decreasing at a given point, take the second derivative of the function in question. Plug in a value for x within the range, or the value of the given point. If the result is positive, the function at that point is increasing, if it is negative then the equation at that point is decreasing.


Rowland, thanx for letting me stretch my mind a little, I haven't had to "flex my skills" for the past nine years. I finished Calculus my junior year of high school, took the equivolency test for college and got all my math credits out of the way. The only recent "mathematics" I've had to take in college was Discrete Math, Stats, Medical Stats, Numerical Analysis, Computational Stats, and Compiler Construct. Theory (which is a computer science class that is strictly number language based). All these "math" classes were for my comp. sci. and major along with the Medical Stats for my Masters in Physical Therapy major. I'd say they were more number theory based classes rather than math classes.

PS. All the things you didn't think you wanted to know about Luder94...hehehe

 

Luder94,

I am sure glad you needed the exercise! I appreciate the help. I am going for a BS in Computer Science at night school and even though I work with software I have never had to use anything like this. Lucky I guess. I graduated from HS in 1976 and used math during my Warrant Officer Training Course (15 or 16 years ago/retired in 1997) but never used math after that. The mind was definately not moving on this problem.

Take care - I am sure glad we have a good mix of folks on the board so that we can help each other out.

 

Wow, we sure do have a good mix of folks. You seem to be pretty established in your occupation, if you don't mind me asking, why are you going after a BS Degree in Comp. Sci. now? From what I've seen in the industry, it seems to me that the ones that haven't gotten the degree are making the most money as programmers and analysts, seeing that they have had more experience than the ones that went to school and got started two to three years earlier than their degreed counterparts.

Hell if I had to do it again and knew then what I know now, I wouldn't have done the Human Biology major and Masters in Physical Therapy degree. I would have finished college in 2.5 years with Comp. Sci. and started working as soon as I could. . .especially at the time period of when I could have come out of college. The earning potential would have risen at least three fold from where I'm at now had I come out of college in 1996....I graduated high school in 1993.

Well anyway, Rowland, keep us posted how night school's going. If there's anything I can try to help with, I'd love to help.

 

Rowland, Wow way to go, still educating! I am an old f*rt now by most standards on this board, got out of HS in '65, but I use calculus just about every day in my job. Luder94 did an excellent job answering your question, so will not espouse on that other than good job! I'm curious, retired Warrent Officer, RA helicopter pilot?

 

MotorMan,
I was one of the oxymoron types - Military Intelligence.
Spent most of my time out and about, you might say, with DIA.