Counter Examples
Mathematics Dictionary
Dr. K. G. Shih
Example | Contents of Mathematics Dictionary
Example | Program ABC Applications of Mathematics Dictionary on Internet
Example | Graphic Samples of Mathematics Dictinary
Subject : Intersections of y = a*x^2+b*x+c with y = p*x+q
Q1. How many intersections of y = a*x^2+b*x+c with y = p*x+q ?
A1. Answer
    * Solve p*x+q = a*x^2+b*x+c
    * This is a quadratic : a*x^2+(b-p)*x+c+q = 0
    * It has no intersection if (b-p)^2 - 4*a*(c-q) less than 0
    * It has one intersection if (b-p)^2 - 4*a*(c-q) = 0
    * It has two intersections if (b-p)^2 - 4*a*(c-q) > 0
Q2. Using WebABC find intersections of functions

    * Program 09 10
    * Program 09 11
    * Program 09 12
Q3. How to use WebABC
    * Step 1 : Enter WebABC and Click Form
    * Step 2 : Click topic 9 in upper box
    * Step 3 : Click program 09 07
    * Step 4 : Back and Click program 09 08
    * Step 5 : Back and Click program 09 09
Remarks
    * The author spent more than 10 years to compile Math Dictionary
    * The system is easy in use and gives thousands applications
    * On this website only some samples are given for demonstration
    * You should have it on your computer
    * Then you can use your computer as a graphic calculator

    * Also you can find many mathematical patterns for school wook
    * For more information, Please contact Dr. K. G. Shih
    * Visit the URL to see more samples
    * Visit the URL to view 105 graphic samples in Program WebABC
    * You can download it and Click file WebABC will run
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