Graphing Polynomial Functions?

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)).

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.

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.

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.

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

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.