Lesson Vertex Form (Page 2 of 2) in pdf

Lesson Vertex Form Page 2

Unit 2 – Quadratic Functions

2.2 – Quadratic Functions (Vertex Form)

Observation: As long as we are dealing with a quadratic whose coefficient in front of the ��

term is ________,

the b or middle term will be ____________. Clearly it is easier to deal with these simpler types of perfect

square trinomials.

5��

− 30�� + 48

At first glance we can definitely see this is not a perfect square trinomial.

Why?

Let’s try factoring out the 5, so that we get the easier coefficient of 1.

Clearly the 48 does not common factor very well, remember we can

common factor part of the expression instead!

Now let’s see if we can CREATE our perfect square trinomial. We’ve got

the ‘a’ and ‘b’ terms, but not the ‘c’ term. (Remember our observation)

We can’t just add things to the expression, we again are merely changing

the presentation, so we must also include the negative ‘c’ term, leaving

no change.

That doesn’t quite look like a perfect square trinomial, let’s take the

negative ‘c’ term outside of the brackets. There was a reason we wrote

our original common factor out front of the bracket, to take terms out of

the bracket, you must multiply.

Finally we have something very close, which does in fact look like a

perfect square trinomial, go ahead and use our trick and simplify.

Examples:

Use the Complete the “Perfect” Square strategy to convert the following into vertex form:

a) 2��

− 12�� + 13

b) 4��

− 12�� + 7

c) −2��

− 5�� − 15

Note: You should start to see a pattern as to what your repeated factor ends up being

HW:

Lesson Vertex Form Page 2