Quadratics can be dealt with in two ways, **algebraically** and **graphically.**

A lot of students see these as two separate topics, however, they do cross over and you can use one technique when dealing with the other.

**The significant points of a quadratic graph**

All quadratic graphs have the same form, they look something like this:

For all quadratic graphs, there are **three **things you need to be able to find using an **algebraic** method - the roots, the y-intercept and the vertex.

In this worksheet, we’re going to look at how we find the **roots algebraically.**

**Example:**

**How to find the roots of the quadratic y = x ^{2} + 3x - 4**

This is actually much simpler than you might think.

We need to think what is important about the two points on the graph above that are labelled root 1 and root 2.

They’re **on the x–axis **which means that the value of y for each of the roots is** y = 0**

So let’s look at what that gives us:

**Step 1: Replace y with zero**

This gives the quadratic equation 0 = x^{2} + 3x – 4 which can be rearranged to x^{2} + 3x – 4 = 0. (Does this look familiar? It should!)

**Step 2: Factorise the quadratic**

You should be able to do this one quite easily:

x^{2} + 3x – 4 = 0 → (x + 4)(x - 1) = 0

**Step 3: Solve the quadratic**

For (x + 4)(x - 1) = 0, we can create two equations:

**x + 4 = 0 → x = -4**

**x – 1 = 0 → x = 1**

So the roots for the quadratic are** x = -4 and x = 1**

It's that simple! Let's have a go at some questions now.