Question

Write the equation of the graph shown below in factored form. the graph starts at the bottom left and continues up through the x axis at one to a maximum around y equals two and goes back down through the x axis at two to a minimum around y equals negative two and back up through the x axis at three

Answer 1

For each x intercept the corresponding factor can be deduced. For x intercepts given at 1,2,3 , the equation can be written as

y= (x-1) (x-2) (x-3)

Because x=1 therefore x-1=0 , similarly x=2 , x-2=0 and , x=3 , x-3=0

or

y= x²+2x-3 (x-3)

or

y= x³+2x²-3x-3x²-6x+9

y= x³-x²-9x+9

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