Question

What is the difference between finding a solution graphically, numerically, and algebraically?

Answer 1

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.

Answer 2

the algebraic method is the only one that will give you an "exact" solution

Answer 3

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.

Answer 4

have you been taught any numerical methods?

Answer 5

Well, the textbook says to use a calculator and use the intersection function, but my teacher says don't use a calculator.

Answer 6

:)

Answer 7

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?

Answer 8

Yes. THat is the problem. lol. I don't exactly know what it means by numerically, so you can see the problem XD

Answer 9

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?

Answer 10

a numerical method is basically some algorithm that guarantees that it will converge to one or more solutions of a given problem.

Answer 11

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.

Answer 12

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. :)

Answer 13

yw :)