We have learned algebraic methods to solve quadratic equations.  We have found the solutions to those equations graphically, and we have also used tables of values to find those solutions.  We now consider the use of programming. 

A basic program to find approximate solutions to quadratic equations by the quadratic formula might look like the graphing calculator program on the left (windows 1-2). 

This program requires three input values a, b, and c, and yields two output values, the solutions of a quadratic equation.  Look at the sample run of the program (windows 3-4). 
Graphing and tables provide such a visual image of the solution.  However, these methods only provide approximate solutions to some equations.  We must use algebraic methods to find the exact value to those equations.   

We can also compute the exact value by a slightly more sophisticated quadratic formula program.  A sample run of such a program is shown in window 5. 
 

Graphing Calculator Explorations

Enter the program listed above into your graphing calculator. Use the program to compute the zeros for the example with values 1, 2, and 4.  If your calculator gives you an error message, check your typing.  If there is still an error, your calculator may not compute imaginary numbers.  What check will we have to build into the program so that problems involving imaginary numbers will not be computed? Write a program to compute the distance and midpoint between two points.