SOLUTION: Is there a way to explain the Quadratic Formula in laymans terms??? I am going to teach Elem. Ed, and is there a simpler way to explain it to my students??? Also, is there any pro

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Question 26: Is there a way to explain the Quadratic Formula in laymans terms??? I am going to teach Elem. Ed, and is there a simpler way to explain it to my students??? Also, is there any proofs for why factoring works?? I've searched and searched, and I cannot find any proofs.
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
The easiest way to become more comfortable with quadratic equations is to be able to generally visualize them as graphs. For example, x%5E2-5x-5 is graph%28+300%2C+200%2C+-5%2C+5%2C+-20%2C+20%2C+x%5E2-5%2Ax-5%29+.
As for a proof of the quadratic formula, you are very right to demand one. It is a pity that they do not include the proof into your curriculum. The idea of this proof is to first shift the curve so that it would become symmetrical around the Y axis. Then it is easy to find where such shifted graph intersects the X axis. Remembering that we shifted it, we know that the solution of the original (not shifted) equation is the solution to our symmetrical equation, shifted back. That's the idea of "completing the square".
It is proven at here. Good luck!