Write x^2 + 10x + 20 in vertex form

Step by step

The question

Question: write y = x² + 10x + 20 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 25 to fill the corner.

And we take 25 away straight after, so nothing changes.

2 Write the square

The full square is x + 5 on each side.

So these three parts are (x + 5) squared.

We write the bracket squared.

The rest stays.

3 Tidy up

−25 plus 20 is −5.

So y = (x + 5)² − 5.

This is vertex form.

4 Read the vertex

In vertex form we need x minus h.

x + 5 is x minus (−5).

So h = −5, and k = −5.

So the vertex is (−5, −5).

Careful!

x plus 5 means h is −5, not 5.

The sign in the bracket is the opposite of h.

5 Check

Let's check: open the brackets again.

(x + 5) squared is x² + 10x + 25.

We get x² + 10x + 20 again.

It works!

Let's look back.

First: complete the square.

Then: write the square.

Then: tidy up.

Then: read the vertex.

Last: check.