• Visualizing the Quadratic Formula

    What would you do if you were asked to solve for x?                  x2 + 8x + 5 = 11

    You would probably set the quadratic equal to zero and try to factor, right?

    Can you factor this quadratic trinomial?             x2 + 8x – 6 = 0           Sadly, no.



    There’s another technique for solving quadratic equations, called Completing the Square. If you can create a perfect square trinomial, you can replace it with the square of the binomial and take the square root. That’s the plan; let’s see how it’s done.

    We have   x2 + 8x + 5 = 11.   Ignore the constants for now, we can deal with those later.

    To make a square, we have to break the 8x evenly in 2 parts. When we do that, we see that the factors must be (x + 4)(x + 4).

    What do we need as a constant? The missing corner is 4 x 4, so we need 16.

    Let’s look at it with algebra.

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    If we can generalize this technique to any quadratic equation, we can create a formula to use to solve for x, every time.

    Hot dog!

    Screen Shot 2014-02-27 at 9.16.03 PM  


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    After lots of algebra…






    We have the Quadratic Formula:Screen Shot 2014-02-27 at 9.16.44 PM