Final answer:
The line of symmetry for the function f(x)=x²-4x-32 is given by the equation x = 2, which is derived from using the formula x = -b/(2a).
Step-by-step explanation:
To find the equation of the line of symmetry for the quadratic function f(x)=x²-4x-32, we need to determine the x-coordinate of the vertex of the parabola. The vertex form of a quadratic equation is y=a(x-h)²+k, where (h,k) is the vertex of the parabola. For a standard quadratic equation ax²+bx+c, the x-coordinate of the vertex, and thus the line of symmetry, is given by the formula x = -b/(2a). In this case, a=1 and b=-4, so the line of symmetry has the equation x = 4/2 = 2.