UNsolving Quadratic Equations & Inequalities
- Judah L Schwartz
The solution of a quadratic equation is a pair of number - let's call them a and b [assume a smaller than or equal to b]. The solution of a quadratic inequality is EITHER all the numbers between a and b, OR all the numbers less than a AND all the numbers greater than b. To UNsolve a quadratic equation or inequality, drag the GREEN dots in the left hand panel to fix the solution set. The right hand panel will show you a quadratic equation or inequality that has that solution set. To see other quadratic equations or inequalities with the same solution set - -- you can use the sliders in the right hand panel to scale the functions or translate them vertically. -- you can use the drag the GOLD dots. Each of the large GOLD dots controls both functions. Each of the small GOLD dots controls only one function. Why is it permissible to change only one function in a comparison of functions? What happens to an inequality when the sign of the scale factor changes? Why? For a given solution set, how many equations or inequalities are there that have that solution set? How do you know? Can you prove it?