Math 12 – Forms of the Quadratic

General Form (a.k.a. "Function Form")

	a : stretch c : y-intercept
Example:	The y-intercept is 4

Transformational Form

	a : stretch k : vertical translation h : horizontal translation (h, k) : vertex x = h : axis of symmetry
Example:	a (stretch) = 2 k (vertical translation) = -3 h (horizontal translation) = 4 The vertex (h, k) is (4, -3) The axis of symmetry is x = 4

Standard Form

This is just like transformational form just changed to y = so that you can enter it into the calculator

Changing from Transformational Form to General Form

Let’s start with this one…

Step 1: Simplify the left hand side of the equation
Step 2: Expand the right hand side of the equation using FOIL
Step 3: Move the constant from the left side of the equation to the right side
Step 4: Divide everything on both sides of the equation by the coefficient of y

Changing from General to Transformational Form

aka “Completing the Square”

Let’s start with one without any stretch… (There is not a coefficient with the “x²” term.)

Step 1: Move the constant at the end to the other side of the equation.
Step 2: Take half the coefficient of the x-term (the “b” value) and square it. Add this square to both sides of the equation and simplify
Step 3: Factor the right side of the equation into a perfect square. Remember, the constant added to the x in both binomial factors is half the “x” term from step 2

A harder one… (There is a coefficient with the “x²” term.)

Step 1: Move the constant at the end to the other side of the equation.
Step 2: Factor out the coefficient of the x^2-term.
Step 3: “Complete the Square.” Take half the coefficient of the x-term and square it. Add this inside the bracket on the right side of the equation. On the left side, add the value multiplied by the value factored out in step 2.
Step 4: Factor the right side of the equation into a perfect square
Step 5: Multiply both sides of the equation by the reciprocal of the stretch factor.
You’re finished! Breath a sigh of relief…