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