Quadratic equations

• What is a quadratic equation?

  Contains terms including $x^2$
• How is a quadratic equation generally written?

  As $ax^2 +$$bx +$$c =$$0$
• What do the letters a, b, and c represent in a quadratic equation?

  They are numbers in the equation
• What are examples of quadratic equations?

  1. $2x^2 - 2x - 3 =$$0$
  2. $2x^2 +$$6x =$$0$
  3. $x^2 +$$2 =$$4$
  4. $3x^2 =$$48$
• How do you solve the equation $3x^2 =$$48$?


  Divide both sides by $3$
• What is the next step after dividing $3x^2 =$$48$ by $3$?


  Square root both sides
• What is the result of $\sqrt{x^2} =$$\sqrt{16}$?


  $x =$$\pm 4$
• What is the principle behind solving quadratic equations by factorising?

  • If the product of two numbers is 0
  • Then one or both numbers must be 0
  • Example: If $ab =$$0$, then $a =$$0$ or $b =$$0$
• What can you conclude if $(x+1)(x+2) =$$0$?


  $x+$$1 =$$0$ or $x+$$2 =$$0$
• What is factorising in the context of quadratic equations?

  Putting expression into brackets
• What is the result of $x(x+3) =$$0$?


  $x =$$0$ or $x =$$-3$
• What are the characteristics of the graph of a quadratic function?

  • Curved graph with a line of symmetry
  • Smooth line with one turning point
  • Graph of $y =$$ax^2 +$$bx +$$c$
• What does it mean if a quadratic graph crosses the x-axis?

  The values of x are the roots of the equation
• What happens if a quadratic equation has one solution?

  The graph touches the x-axis without crossing
• What does it indicate if a quadratic equation has no solution?

  The graph doesn't touch or cross the x-axis
• How can roots be found graphically for a quadratic function?

  • Draw the graph of $y =$$ax^2 +$$bx +$$c$
  • Solutions are x-coordinates where it crosses the x-axis
• What are the roots/solutions of the quadratic equation $x^2 +$$x - 6 =$$0$?


  $-3$ and $2$
• How do you factorise the equation $x^2 +$$x - 6 =$$0$?


  It gives $(x + 3)(x - 2) =$$0$
• How can you check the solutions of a quadratic equation?

  By using the graph method