Posted by **Kim** on Wednesday, November 18, 2009 at 10:28am.

If you have an arbitrary polynomial P(x) of the n’th degree in x, and you graph the equation y = P(x), describe the overall shape of this graph. What happens when x gets large in the positive and negative directions, and how many peaks and valleys does the graph have? How many times does the graph cross the x-axis? (To simplify, let the sign of the highest power term in P(x) be positive.) Hint: See chapter 11 of the text.

- Algebra 2 -
**drwls**, Wednesday, November 18, 2009 at 10:47am
I recommend that you read chapter 11 and take a stab at this yourself.

In general, what happens at very large values of x and -x depends upon the sign of the highest order term, x^n, and whether n is evn or odd. The higher the value of n, the more times the function goes up and down, but the number of maxima, minima and zeroes will depend upon the coefficients of all terms. An nth order polynomial can have n roots, but some may be equal and some may be complex numbers. Complex roots come in conjuagate pairs.

## Answer This Question

## Related Questions

- Algebra - 1.Write the equation of a line that is perpendicular to the given line...
- math - What happens to y as x gets larger? What happens to x as y gets larger? d...
- Geometry HELP!!! - What happens to the graph of the line y = 3x -2 when the ...
- MATH TRIGONOMETRY - refer to the polynomial function f(x)= -x(x-1)(x+2) in ...
- Algebra - Write an equation for a function at has a graph with the given ...
- College Algebra - 1.Answer the following for the given quadratic function. f(x...
- Algebra - Below is the graph of a polynomial function f with real coefficients. ...
- log - what happens to the shape of the graph of f(x)=b^x when b=1? what happens ...
- Algebra - How can you tell an equation's real or imaginary roots just from its ...
- College Algebra - Help! Write the equation of the function that has a graph the...

More Related Questions