text: # 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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