A quadratic function has equation F(x) = x ​2 - x - 6 Determine the x-intercepts for each function

Not sure I understand your question....can you clarify?

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 .