2. First you determine the degree by the end behavior, or the exponents. And decide wether its an odd or even number. For example in the problem above there are exponents 2, 1, and 3 so the degree is 6. Which is an even number. The degree of the polynomial is absolutely key to graphing it. The degree tells a good amount of information about the graph. The first thing it tells us is the general shape of the polynomial, such as does it start from the bottom and continue to the top, or does it start at the top and curve its way back to the top? The second thing it tells us is the number of possible x-intercepts the graph might have. The end behavior of a polynomial function is a description of how the polynomial behaves as it approaches positive and negative infinity. In other words, what does the polynomial do at the two ends of the graph? Some go up to infinity on one side and down to negative infinity on the other. Some have each end go to positive infinity. The end behavior is totally dependent on the leading term of the polynomial function when simplified
3. Positives This shape results if the leading term is positive and the degree of the polynomial is even. An example would be y = 2x2+4x-3. The degree of the equation is 2 (even), and its leading coefficient, 2x2, is positive.
4. Negatives This shape results if the leading term is negative and the degree of the polynomial is even. An example would be y = -2x4+3x3+x-7. The degree of the equation is 4 (even), and its leading coefficient, -2x4, is negative.
