Completing the Square

Hey everyone! Brianna here.

Today we had a pretty important lesson so I'll try not to make it too long.

The first thing we did was a pattern activity, where we were reminded of FOIL and the patterns in factoring perfect squares. We also learned about what a perfect square actually looks like.

Take this equation for example:

If we were to look at this as an actual square, this is what it would look like:

(Made by myself in Photoshop)

We then went into our booklet and started to fill out "Transformations of Quadratic Functions 1" where we learned what the term completing the square means.

We are now familiar with two forms of the quadratic function:

1.

2.

When a quadratic function is represented in the first form, it is usually converted to the second form so that it is easier to define the characteristics. This is what completing the square is called.

Let's try one:

Complete the square

Step 1: Substitute for y=0.

Step 2: Take the c value to the other side.

Step 3: Take the b value, divide by 2 and square it.

Step 4: Take the calculated value and add it to both sides of the equation.

Step 5: Factor the perfect square, move the c value back and equate everything to y.

Congratulations! You've just completed the perfect square.

This post is getting pretty long, so I will post a second scribe that sums up factoring to find zeros.