Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
Course: Algebra III / Intermediate Algebra
Topic: Functions and Graphs II
Subtopic: Parabolas II - Graphical Approach


In this lesson we continue to explore parabolas, given in both the standard form y=a(x-h)2+k and the general form y=ax2+bx+c. This lesson covers analyzing these equations graphically and producing the graphs electronically. We are also able to use this information to solve some basic optimization application problems (e.g., optimize profits in a small business).

Be sure to play/explore with your grapher what happens to the basic parabola y=x2 when you put a negative in front, a coefficient other than 1 in front, add/subtract a number to the x2 (as in x2 ± #), add/subtract a number to the x (as in (x ± #)2). Watch for the effects on the shape of the graph, vertex, and axis intercept points.


By the end of this topic you should know and be prepared to be tested on:


Define: point vs. value, minimum point, maximum point, extrema point, optimization problem

Text Notes

Depending on the text, they may in this section go too far (in my opinion) into the realm of precalculus. Don't freak out! There is a good chance you can skip some of the more difficult examples and problems. Also take advantage of technology! Here are some notes:

Supplemental Resources

It is recommended that you be able to use a calculator (handheld or software) to solve the optimization problems covered in this lesson. If you have a handheld graphing calculator then these sites may help:

READ: Once you are able to use your grapher to locate an extrema point read my Lecture - An Application of Quadratic Functions and try to follow along on your own grapher.