The graph of the function f x 6x3 6x2 3x 18 can be trans

The graph of the function f (x) = 6x^3 - 6x^2 - 3x + 18 can be translated horizontally t units to eliminate the quadratic term - that is the result should be of the form g(x) = x^3 + px + q. Find the value and the direction for t.

Solution

(a -b)^3 = a^3 - b^3 -3a^2b +3ab^2

f(x) = x^3 - 6x^2 - 3x +18

comparing : 3a^2b = 6x^2 ; a = x ; b = 2

= x^3 - 8 - 6x^2 +12x -12x +8 -3x + 18

= (x -2)^3 - 15x +26

on comparing we get p = -15 ; q = 26 ;

horizontal shifting of 2 units