How do you model an equation such as 4+x^2-9=14?

Question

I learned how to model equations with variables on one or both sides (like 2x-9=4x-29), and the power of the variable is one.

But I'm wondering, how can you model equations where the variable is squared, cubed, or such?

Answer 1

Not sure what you mean by model an equation, do you mean to solve it in general? The quadratic formula for solving quadratics in general is well known, also there is a formula for solving cubics in general, this formula is very unweildy and not as well known.
http://www.math.vanderbilt.edu/~schectex/courses/cubic/
I just searched on the phrase "how to model an equation" and turned up very little. I turned up equation models for specific situations but nothing about modelling equations per se. This confirms my suspicion that you are using non standard terminolgy and so making your question unclear.
If by modelling an equation you mean to graph it, this would be done by finding a few points that fit the equation, plotting them, and then filling them in with the shape that is known to correspond with that type of function. Plotting points around the intercepts and asymptotes is helpful, you learn to do this in HS or college algebra. A graphics calculator helps here but don't be overly dependant on it, you need to understand where the graph comes from and to understand this it's good to do some graphs by hand.
Generally, we use equations to model situations. So if you mean, how to develop a higher order equation to model a situation, generally you need as many constants as the order of the equation, plus one. For example if you want a model involving a squared varialbe you'd need three constants from the situation (such as starting value and one value at time t not equal to 0) to develop an equation to describe your situation.
http://members.tripod.com/martharhodes_1/id18.html
http://www.learner.org/channel/workshops/algebra/workshop4/index.html
If you want a model involving a cubed varialbe you'd need four constants, etc.
To develop logarithmic and exponential models for a situation you'd again need at least two constants.
http://216.109.125.130/search/cache?ei=UTF-8&fr=slv8-dyc&p=how+to+find+an+exponential+model&u=wcherry.math.unt.edu/math1650/exponential.pdf&w=exponential+model&d=Yi9cFkVuN2KX&icp=1&.intl=us
http://www.gypsymoth.ento.vt.edu/~sharov/PopEcol/lec5/exp.html
Then you'd use these constants in a system of n equations in n unknowns to develop the coeffieicnts for your model.
In regression analysis, a topic in statistics, we develop equation models for various situations. These models are linear when a linear model is adequate, although they may involve several coefficients, one for each relevant variable.
http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm
This is as far as I want to go with this, as your question is not clear. Please clarify it and maybe you can get a better answer.

Answer 2

I hope you mean on a graph. If so, then it will be in the shape of a U. you have to get y alone. Therefore it comes out as x^2-19=y. So then you start your graph at negative 19. Then for x coordinates 1 and -1 you move one up (because 1^2 is 1 and -1^2 is 1) For x coordinates 2 and -2 your y-coordinates would be 4 and 4. So whatever x is, you square it and that's your y-coordinate.

Answer 3

u r reffering to the word problem it will be mentioned as the age of A varies with the sq of the age of B then u know
A=kB^2
where k's a const
hope it helped