anonymous
  • anonymous
What is the difference between finding a solution graphically, numerically, and algebraically?
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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asnaseer
  • asnaseer
example: find the solutions to x^3 + 3x^2 -17x + 9 = 0 1. graphically: draw a graph and observe where it crosses the x-axes 2. numerically: use the Netwton-Raphson method to iterate to each root starting with a guess 3. algebraically: use the formula for cubic equations to find the roots.
asnaseer
  • asnaseer
the algebraic method is the only one that will give you an "exact" solution
anonymous
  • anonymous
Well, it's mainly my trouble of differentiating between numerically and algebraically because I have to find the solution both ways...the actual problem involves a sinusoid and the line y = 6. I can solve for x in the equation, but I don't know what the numerical way would be.

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asnaseer
  • asnaseer
have you been taught any numerical methods?
anonymous
  • anonymous
Well, the textbook says to use a calculator and use the intersection function, but my teacher says don't use a calculator.
asnaseer
  • asnaseer
:)
asnaseer
  • asnaseer
so, just to be clear, you have something to solve and you know how to solve it algebraically but are looking for a way to solve it numerically without using a calculator?
anonymous
  • anonymous
Yes. THat is the problem. lol. I don't exactly know what it means by numerically, so you can see the problem XD
asnaseer
  • asnaseer
well in this case I would say your teacher may have made a mistake. for a numerical solution you need to use some method that eventually iterates to the correct answer. one such method is the Newton-Raphson method (described here: http://en.wikipedia.org/wiki/Newton%27s_method). some calculators have this built-in, so you can just enter the equation that needs solving and they will execute the most appropriate numerical algorithm to get the answer. does that explain it better?
asnaseer
  • asnaseer
a numerical method is basically some algorithm that guarantees that it will converge to one or more solutions of a given problem.
asnaseer
  • asnaseer
each algorithm has its restrictions - so you need to make sure the problem you are solving satisfies the restrictions of the algorithm otherwise it will not converge to a solution.
anonymous
  • anonymous
Well, I guess that I'll just ask my teacher tomorrow since I never learned that method. I think I understand what it means to solve numerically now, but I think that we do indeed need a calculator now...I'll see tomorrow. Thank you. :)
asnaseer
  • asnaseer
yw :)

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