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Deriving the Quadratic Formula. Use the complete the square method: Step one divide through by “a ”. Then isolate the terms with x (move everything else to the other side of the equal sign). - PowerPoint PPT Presentation
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Deriving the Quadratic Formula
Use the complete the square method: Step one divide through by “a”
Then isolate the terms with x (move everything else to the other side of the equal sign)
Then “complete the square” by taking half of the coefficient of x and then squaring it and add it to both sides of the equation:
Combine Information on Right Side
• In order to combine the information on the right of this equals sign we need to have a common denominator. The common denominator will be 4a2 so we will have to multiply the numerator and the denominator of c/a by 4a.
Multiply the numerator and the denominator of c/a by 4a.
On the left of the equals sign of this equation is a perfect square so we can rewrite it as x + half of the coefficient of x)2.
Since we are solving for x and x is being squared we now need to take the square root of both sides:
We broke the denominator (4a2) out under its own square root since it is a perfect square and we can take the square root of it and write it as 2a
We now need to isolate x:
Since we already have a common denominator we can combine these terms and arrive at the quadratic formula
• Resources:• https://www.cdli.ca/learning-resources/mlos/mathematics-
tutorials/unit-13.html