## Monday, September 16, 2013

### SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

Equation:
f(x)= x^4-5x^3+3x^2+9x

This problem is about is to see if you can use what you know about polynomials to make an accurate graph of it.  To solve it, you must need to know and understand how to factor a polynomial, the end behavior of certain polynomials, how to find the x-intercepts with multiplicities, the y-intercept, and how to graph the zeroes.

If you want to make your graph even more accurate, then you can find and use the extrema of the graph. In addition, be careful to make sure the end behavior is correct and the zeroes are correctly plotted. If a zero has a multiplicity of 1, then the graph goes through the point. If a zero has a multiplicity of 2, then the graph bounces off the point. Finally, if the zero has a multiplicity of 3, then the graph curves through the point. Make sure that all your zeroes match up to the highest degree (exponent).

1. Since we chose the zeroes(x-intercepts) first, multiply all the factors to get the equation.
2. Make note of the end behavior and how the graph will approach a zero (Thru, Bounce, Curve).
3. Find the y-intercept by plugging in 0 for x in the equation and plot it.
4. Draw the graph.