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A quadratic function has equation F(x) = x2- x - 6
Determine the x-intercepts for each function

a).    Y=f(-3x)

Guest Feb 20, 2018
 #1
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Not sure I understand your question....can you clarify?

ElectricPavlov  Feb 20, 2018
 #2
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y  =  f(-3x)      The  x-intercepts of this function are the values of  x  when  y = 0

 

The  x-intercepts are the  x  values that make this equation true:

 

0  =  f(-3x)

                                    Since  f(x)  =  x2 - x - 6  ,   f(-3x)  =  (-3x)2 - (-3x) - 6

0  =  (-3x)2 - (-3x) - 6

 

0  =  9x2 + 3x - 6

                                    Divide through by  3 .

0  =  3x2 + x - 2

                                    Factor the right side.

0  =  3x2 + 3x - 2x - 2

 

0  =  3x(x + 1) - 2(x + 1)

 

0  =  (x + 1)(3x - 2)      Set each factor equal to zero.

 

x + 1  =  0       or       3x - 2  =  0

x  =  -1            or         x  =  2/3

 

The x-intercepts are  -1  and  2/3 .

hectictar  Feb 21, 2018

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