Graphing Polynomial Functions?

Question

Does anyone know how to graph a polynomial function(either cubic-3 or quartic-4) by hand w/out a calculator, or how to read these graphs?

Answer 1

If you take Calculus, you learn some more guidelines on how to graph functions.

I'm assuming your current methods are calculating the x and y intercepts and asymptotes, but with Calculus you can find out things such as intervals of increase and decrease, local minima/maxima, intervals of concavity ...

This is not only true for cubic and quartic functions, but even for strange functions like x/e^x or sqrt(ln(x)).

Answer 2

Set up a table with 2 columns, one for x values and one for y values. Choose the x values and calculate the y values, entering each in the table. Then plot the points on graph paper. You may have to use a scale factor for cubic or quartics, as the values tend to increase rapidly. Factoring or differentiating the functions, if you can, will give clues on what x values to choose.

Answer 3

If you graph them by hand you have to make a table of x's & y's and calculate each point manually then plot the points on a piece of graph paper. If you want to cheat, you can enter the polynomial function into your calculator and it can tell you x & y values based on the increment you tell it (every 1, every 0.1, etc). Other than this, I don't think there are any easy ways to do it.

Answer 4

The most important thing to look at is the highest order term. This determines the behavior for large x. You look at both the coefficient and the even/odd of the exponent.

If it has an odd exponent, then it crosses the x axis at least once. I.e., it has at least one real root.

An even exponent, and a positive coeff, then it looks like a concave up parabola for large |x|.

An even exponent and a negative coeff: it looks like a concave down parabola for large |x|.

If the constant is zero, then x=0 is a root, otherwise the constant is the value at x=0 since

p(x=0) = the constant of the polynomial.

There are also a whole bunch of things that people discovered before computers made us all lazy. Check out wikipedia's math section for more details.

Answer 5

Plug in values for x whilst x=0, y=2(0)^5 + a million = 2(0) + a million = 0 + a million = a million so plot the factor (0,a million) now attempt x=a million, y=2(a million)^5 + a million = 2(a million) + a million = 2+a million = 3 so plot (a million,3) plugging in x=-a million, y=2(-a million)^5 + a million = 2(-a million)+a million = -2+a million = -a million so plot (-a million,-a million) connect the factors and strengthen the curve in the two instructions

Answer 6

Simple Algebra:

2x3rd power +7x2nd power+4x +2. To deal with factors such as this you must remember your beginning, you know, metric system, cubic measure, weight etc.... go back one step to algebra 1-2 then fractions, your answer are there.