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The Quadratic Formula
is the popular formula used to determine
the roots of a quadratic equation. But where
did it come from? Let’s explore how exactly
the quadratic formula is derived.
First, in order to use the quadratic formula,
the equation must be in the standard form:
Now divide the equation by a:
Next, we will do a substitution:
And the equation becomes:
This new version of the equation is in standard
form for CTS (Completing The Square). Plugging
the appropriate symbols into the CTS formula
gives:
Let’s solve for x:
Now re-insert the values we substituted
for earlier:
Finally, multiply all terms under the radical
by a2 and divide
outside the radical by a.
Re-arranging the equation produces something
more familiar-looking:
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