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Private Notes
Two robots begin to explore quadratic equations, discovering basic ideas that are not usually shown in print. Once the standard form is found, the robots get a feel for the quadratic equation by tossing a ball between each other. This helps them realize every quadratic equation, when graphed, forms a parabola.
In a factory, the robots start to understand the factoring method for solving quadratic equations. Once again, they learn standard form is needed for factoring. When all is said and done, the robots keep running into ""rejects.""
One of the robots wants to complete the square before factoring the quadratic equation. What is found, revolutionizes the whole process. Completing the square, and reverting to square roots, will solve any quadratic. One string is attached: Completing the square only works when the quadratic begins, x squared.
The robots want to find a general formula for solving any quadratic, and this is it:x squared = -b plus or minus the square root of b squared minus 4ac over 2a.It looks like a mess, but when used, the quadratic formula is a major tool, even if the square root of one variable is not a rational number.
After a quick review of the lessons learned in the first four shows, this program concentrates on the discriminant:the square root of b squared minus 4acIt is the discriminant that dictates where the parabola lies on the Cartesian plane–if the parabola touches the x-axis in two points, one point, or not at all.The greatest challenge occurs when the discriminant is negative–forcing the use of complex numbers. This is a combination real number and the imaginary number (labeled i).
The robots are ready to apply what they have learned about solving quadratics. It leads up to a parabolic jump over a canyon à la Evel Knievel. Turns out parabolic structures occur all the time–in bridges, the SkyDome, car headlights, dish antennas, and telescopes. This program also discusses how computer games use the quadratic formula to show where a projectile–be it a golf ball or an arrow–has landed.
