Quadratic with zeros 2 and -2

Step by step

The question

Question: write a quadratic with zeros 2 and −2.

A zero of f is an x that makes f(x) equal 0.

1 Each zero gives a bracket

If c is a zero, then x minus c is a factor.

Put c in, and that bracket is 0, so all of f(x) is 0.

The zero 2 gives x − 2.

Next, −2 gives x − (−2).

Minus a minus is plus: x + 2.

Careful!

The sign flips.

The zero 2 gives x − 2, because that is 0 when x is 2.

2 Write f(x)

So f(x) = (x − 2)(x + 2).

3 Multiply out

Each part of the first bracket times each part of the second.

(x − 2) times (x + 2).

Each part times each part.

Like terms together: x² − 4.

So f(x) = x² − 4.

4 Check

Let's check: put each zero in.

First x = 2.

We get 0.

And x = −2.

We get 0.

Let's look back.

First: each zero gives a bracket.

Then: write f(x).

Then: multiply out.

Last: check.