Outcomes
In this lesson you will learn
- to solve polynomial equations and inequalities by examining the graphs of the corresponding polynomial functions
- how to find the local maximum and local minimum values of a polynomial function
By the end of this section students will be able to:
- analyze relations, functions and their graphs
- use tables and graphs as tools to interpret expressions
- analyze and solve polynomial, rational, irrational, absolute value and trigonometric equations
- analyze and solve polynomial, rational, irrational and absolute inequalities
- model real-world phenomena with a variety of functions/relations
- determine the equations of polynomial and rational functions
- factor polynomial equations
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- how to graph cubic and quartic functions
- how to solve quadratic equations and inequalities by examining the graph of the quadratic function
- the shapes of the graphs of cubic and quartic functions
- the effect the degree of a polynomial has on the maximum possible number of real roots
- the "zero principle"
- the relationship between the roots of a polynomial equation and its factors
- how to find the surface area of a box (for #18)
- formula for volume of a box (for #17)
- formula for volume of a cylinder (for #23)