Topic outline

  • Outcomes

    Collapse all Expand all


    In this course you will learn how to: 

    1. Solve quadratic equations by factorisation.
    2. Solve quadratic equations by using the quadratic formula.
    3. Solve simultaneous equations involving quadratic equations.
    4. Solve word problems involving quadratic equations.

  • Solve quadratic equations using factorisation

    What are quadratic equations?

    A quadratic equation is an equation which is written in the form \(a{x }^{2}+bx+c=0 \) where \(a\), \(b\) and \(c\) are constants and the highest power of \(x\) is \(1\).  \(a{x }^{2}+bx+c=0 \) is called standard form.

    Here are examples of quadratic equations:

    • \(3{x }^{2}+x-2=0 \) Standard form
    • \(a(a-2)=5\) Expand first to get equation into standard form
    • \(\frac{4}{x+1}-1=x\) Multiply through by the L.C.D and simplify to get the equation in standard form

    You must have a good understanding of factorising trinomials before you start this topic. Revise factorisation by clicking on: Factoring Quadratic Expressions.

    • Zero product property

      To solve a quadratic equation by factorisation we need to apply the zero product property. 

      If A times B is equal to zero then A=0 or B=0.

    • Steps to solve a quadratic equation 

      You can learn the steps to solve a quadratic equation by factorising by clicking on this textbook or by watching the next video. 

    • Quiz icon
      Practise using factorisation to solve equations Quiz

  • Use the quadratic formula to solve equations

    When to use the quadratic formula

    The quadratic formula can be used to solve any quadratic equation, even those that can be easily factorised. However, solving quadratic equations by factorisation is still the simplest and quickest method. So, use factorisation whenever you can. But, as long as you know the values of \(a\), \(b\) and \(c\) you can use the quadratic formula.

    Before, you learn about the quadratic formula you should understand how to complete the square. The quadratic formula is easily derived from a quadratic equation is standard form by completing the square. The video explains the steps of completing the square using a visual perspective. 

    • Deriving the quadratic formula

      The quadratic formula can be easily derived by using the method of completing the square. This method is explained in the next video. 

      If you'd like to refer to a text-based proof you can find that here: Quadratic Formula proof review.

    • Practise using the quadratic formula

      To practise using the quadratic formula, try this next activity: Quadratic formula. 

  • Simultaneous equations

    In equations with two or more unknown variables we use simultaneous equations to solve for the unknowns. We can solve equations simultaneously in the following ways:

    • Algebraically using either the method of elimination or substitution.
    • Graphically by drawing the graphs and finding the point where they intersect.

    • Solve simultaneous equations by substitution

      Watch the next video for examples of the method of substitution to solve simultaneous equations involving quadratic equations. 

    • Solve simultaneous equations graphically

      We can find the solution to a system of equations graphically by drawing the graphs and finding the point(s) of intersection. The next video explains this concept using an example. 

    • Working with simultaneous equations

      Practise solving simultaneous equations graphically and by substitution by trying this activity: Quadratic systems.  

  • Word problems involving quadratic equations

    To solve a word problem you need to be able to change the given information into mathematical statements and equations. There are some steps that you can follow to help you work through word problems more effectively. You can read through these steps in: Word Problem Strategies.