# 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.

Key stage:  KS 4

Year:  GCSE

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:

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 = 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.

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• National Tutoring Awards 2023 Shortlisted
• Winner - Private Tutoring
• Finalist
• Winner - Best for Home Learning / Parents
The text passage provides an overview of how to find the roots of a quadratic equation using algebraic methods, with a step-by-step example. It does not contain a specific mathematical question or an answer to a question.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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.

Key stage:  KS 4

Year:  GCSE

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:

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 = 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

Try an activity or get started for free

• National Tutoring Awards 2023 Shortlisted
• Winner - Private Tutoring
• Finalist
• Winner - Best for Home Learning / Parents
user
The text passage provides an overview of how to find the roots of a quadratic equation using algebraic methods, with a step-by-step example. It does not contain a specific mathematical question or an answer to a question.

TYPE: NO_QUESTION