Deriving the Quadratic Formula

Ever wanted to dazzle your friends by deriving the quadratic formula for them? Now you can! Just follow these simple steps and your friends will soon be in awe of your wicked algebraic skillz.

	Start with the general form of the quadratic function and let y = 0.
	Subtract c from both sides
	Factor out the stretch (the “a” coefficient)
	Complete the Square and factor it.
	Simplify the left side of the equation. Find a common denominator and group the terms together.
	Move the stretch to the right side of the equation. (Divide both sides by a).
	Take the square root of both sides of the equation.
	Subtract the b/2a from both sides.
	Group like terms and you’re there!

From General to Transformational Form… Deriving h = -b/2a

Today we showed in class that the x-coordinate of the vertex of a quadratic function in general form is given by -b/2a.  (p48 #26).  Below is a proof of why this is always true.  Just complete the square to change general form into transformational form.

	Start with the general form of the quadratic function.
	Subtract c from both sides
	Factor out the stretch (the “a” coefficient)
	Complete the Square and factor it.
	Simplify the left side of the equation. Find a common denominator and group the terms together.
	Move the stretch to the right side of the equation. (Divide both sides by a).
Vertex	We can use transformational form now to find the vertex. h = -b/2a