Turning points - polynomials, Algebra

Assignment Help:

The "humps" where the graph varies direction from increasing to decreasing or decreasing to increasing is frequently called turning points.

 If we know that the polynomial contains degree n then we will know that there will be at most n -1 turning points in the graph.

Whereas this won't help much with the actual graphing procedure it will be a nice check.  If we contain a fourth degree polynomial with five turning points then we will know that we've done something incorrect as a fourth degree polynomial will contain no more than 3 turning points.

Next, we have to explore the relationship among the x-intercepts of a graph of a polynomial and the zeroes of the polynomial.  Remember again that to determine the x-intercepts of a function we have to solve the equation

Also, remember again that x = r is a zero of the polynomial, P ( x ) , provided P ( r ) = 0 .  However this means that x = r is also a solution to P ( x ) = 0 .

In other terms, the zeroes of polynomial are also the x-intercepts of the graph. Also, remember again that x-intercepts can either cross the x-axis or they can only touch the x-axis without in fact crossing the axis.

Notice as well through the graphs above that the x-intercepts can either flatten as they cross the x-axis or they can go by the x-axis at an angle.


Related Discussions:- Turning points - polynomials

Non liner functions, what is a word problem for a nonlinear function?

what is a word problem for a nonlinear function?

AS/A2 Coursework, I need to do a coursework for math but do not know what t...

I need to do a coursework for math but do not know what to do?

Equations reducible to quadratic form, In this section we are going to look...

In this section we are going to look at equations which are called quadratic in form or reducible to quadratic in form . What it means is that we will be looking at equations th

Math, are these like terms

are these like terms

Graphing cubic functions, how to graph f(x)=-x to the 3rd minus 3 using tra...

how to graph f(x)=-x to the 3rd minus 3 using transformations

Equivalent Ratios and Graphs, A car travels at a rate of 50 miles per hour....

A car travels at a rate of 50 miles per hour.Use equivalent ratios to graph the distance the car travels over time.Graph time on the x-axis and distance on the y-axis

Evaluating radical expressions, Express the answer as an integer, simplifie...

Express the answer as an integer, simplified fraction, or a decimal rounded to two decimal places.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd