Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Use Algebra to Identify the Roots of a Quadratic

In this worksheet, students will practise using factorisation to find the roots (solutions) for a quadratic graph.

'Use Algebra to Identify the Roots of a Quadratic' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel,

Curriculum topic:   Algebra, Graphs of Equations and Functions

Curriculum subtopic:   Graphs Graphs of Equations and Functions

Difficulty level:  

Worksheet Overview

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:

 

Quadratic graphs

 

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.

 

A quadratic graph

 

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 = x2 + 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 = x2 + 3x – 4 which can be rearranged to  x2 + 3x – 4 = 0. (Does this look familiar? It should!)

 

Step 2: Factorise the quadratic

You should be able to do this one quite easily:

x2 + 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.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free

  • educational
  • bettfutures
  • cxa
  • pta
  • era2016
  • BDA award
  • Explore LearningTuition Partner
  • tacm