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```					Quadratic equations

A review
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

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
   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
work?
   (x+2)2 = x2 + 4x + 4
   You should recognise that the right
hand side is a perfect square- a
   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
    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
   Remember this:
   Ok let’s prove this using the method
of completing the square.
   An animation deriving this

   Some examples here
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
   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.
   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
   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?
   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
   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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