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Quadratic equations Quadratic equations

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					Quadratic equations

       A review
Factorising Quadratics to solve!-
          four methods
 1) Common factors you must take out any
  common factors first x2+19x=0
 x(x+19) = 0       x= 0,-19
 2) Recognition these are called cookie

  cutters (a+b)2, (a-b)2 or
                       (a+b)(a-b)=0
Proof to perfect square
 Proof to difference of two squares

 3) Cross method

 4) Quadratic formula
      A warm up activity- solve the
              following
   1) x2+6x+5=0

   2) x2-3x-40=0

   3) X2-9=0

   4) x2-11x=0

   5) x2-169=0

   6) 9x2-25=0
              Homework
   16th January
   Ex 23, 24, Quadratic Formula 25
   Choose all or odd questions
       Cross Method- Factorising
              Quadratics
   Solve x2 +15x+56 = 0
   There are three steps to follow:
   Step 1 draw a cross and write the factors of 5m2



   Step 2 write down the factors of the constant 56 so that
    cross ways they add up to the middle term which is 15x.
    Remember here the sign of the constant is very important.
    Negative means they are different and positive means the
    signs are the same
   Step 3 write from left to right top to bottom the factorised
    form.
    Another example using cross
              method
   Solve : x2-3x-40 = 0

   The minus 40 tells me the factors
    have different signs.
    Yet another example of cross
              method
   Solve x2+3x-180=0
     How does the cookie cutter
              work?
   (x+2)2 = x2 + 4x + 4
   You should recognise that the right
    hand side is a perfect square- a
    cookie cutter result
   There are three cookie cutter results
   What are they?
            Perfect Square
   Look at this: what is (a+b)2 =?
                 a          b

       a



       b
    There are many ways to solve
        quadratic equations
    Factorise any common factors first!
   A) Cross method
    B) Standard results cookie cutters
   Now we are going to look at:

   C) solving quadratics by using the
    quadratic formula!
       The Quadratic formula
   Remember this:
        The Quadratic formula
   Ok let’s prove this using the method
    of completing the square.
   An animation deriving this

   Some examples here
       The Quadratic Formula
   Using the quadratic formula.
    Sometimes you cannot use the cross
    method because the solutions of the
    quadratic is not a whole number!
   Example solve the following giving
    you solution correct to 3 sig fig
   3x2-8x+2 = 0
     Solving quadratic equations
   Example 1 Solve x2 + 3x – 4 = 0




   Example 2 Solve 2x2 – 4x – 3 = 0
   This doesn’t work with the methods we
    know so we use a formula to help us solve
    this.
             Quadratic formula
   Form purple math an intro



   A song

   Where does it come from?
               Example
   Example Solve 2x2 – 4x – 3 = 0
   a = 2, b = -4 and c = -3
      Using you brain!
   Only use the quadratic formula to solve
    an equation when you cannot factorise
    it by using
   A) cookie cutter
   B) cross method
        Some word problems
   The height h m of a rocket above the
    ground after t seconds is given by
    h =35t -5t2. When is the rocket 50
    m above the ground?
        Quadratic inequalities
   Solve x2-x-2<0
   Firstly draw a sketch by factorising
   Look at the sketch and see what
    region is below the axis?
           Another example
   Solve the following X2 - 5x+6 > 0
              Classwork
   Complete ex 28 manually, 28* using
    Autograph.
      Using other graphs to solve
              quadratics
   Draw the graph of y = x2. Use this
    graph to solve
   1) x2= 5             x2-5 = 0
   2) x2= -3             x2+3 = 0
   3) x2= x or this is the same as
       x2-x = 0
   4) x2= x+1 or x2-x-1=0
    Solving simultaneous equations-
             one non linear
   Draw the graph y = x2 – 5x +5 for 0<x<5. Use
    this to solve:
   x2 – 5x +5 = 0


   x2 – 5x +3 = 0


   x2 – 4x + 4 = 0


   Homework Exercise 30

				
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