Write y = x^2 - 2x - 8 in vertex form

Step by step

The question

Question: write y = x² − 2x − 8 in vertex form.

Vertex form is a times (x minus h) squared, plus k.

The vertex, the turning point, is (h, k).

1 Complete the square

We add 1 to fill the corner.

And we take 1 away straight after, so nothing changes.

2 Write the square

The full square is x − 1 on each side.

So these three parts are (x − 1) squared.

We write the bracket squared.

The rest stays.

3 Tidy up

−1 minus 8 is −9.

So y = (x − 1)² − 9.

This is vertex form.

4 Read the vertex

In vertex form we need x minus h.

x − 1 is x minus 1.

So h = 1, and k = −9.

So the vertex is (1, −9).

Careful!

x minus 1 means h is 1, not −1.

The sign in the bracket is the opposite of h.

5 Check

Let's check: open the brackets again.

(x − 1) squared is x² − 2x + 1.

We get x² − 2x − 8 again.

It works!

Let's look back.

First: complete the square.

Then: write the square.

Then: tidy up.

Then: read the vertex.

Last: check.