Chapter 14: Quadratic Equations and Formulae

Equations

• Quadratic equations can be written in the form ax^2 + bx + c = 0 where a,b and c are numbers
• You need to be able to solve a quadratic equation without using your calculator
  • Rearrange it into the form ax^2 + bx + c = 0
  • Factorise the left-hand side
  • Set each factor equal to zero and solve to find two values of x

Worked it out

• Follow the three steps given above
• The equation is already in the right form sometimes
• To factorise look for two numbers which add up to the 2nd number and multiply to make the 3rd number
• Set each factor equal to 0 and solve
• When you are solving a quadratic equation you must rearrange it into the form
• Be really careful if the coefficient of x^2 is bigger than 1
  • When you are solving an equation`you must always show clear algebraic working
  • Don’t just write down the answers without any working

Quadratic Formula

• The solutions of the quadratic equation ax^2 + bx + c = 0 where a not= 0 are given by

  

  • You can use this formula for any quadratic equation
  • But be careful, not all quadratic equations have a solution

Checklist

• Equation is in the form ax^2 + bx + c = 0
• Write down your values of a.b and c before you substitute
• Use brackets when you are substituting negative numbers
• Show what you have substituted in the formula
• Simplify what is under the square root and write this down
• The +- symbol means you need to do two calculations

Working it out

• You are asked to find solutions
• This tells you that you are solving a quadratic equation
• You must give your answer correct to the certain amount
• Write down at least 5 figures after the decimal point on the calculator display before giving your final answer
• You might need to use the S-D button on your calculator to get the answer as a decimal