Subject: Deriving the Quadratic Formula

Name: James

Who is asking: Student

Level: Secondary

Question:

How do you derive the quadratic formula? I know what it is, but the textbook doesn't say how to derive it.

Hi James

The quadratic formula is derived by "completing the square". Suppose you have the general quadratic equation

Divide both sides by a to get

or

By adding the square of one half the coefficient of x to both sides, the left side becomes a square, that is

or

.

Thus

,

and finally

Cheers,

Penny

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