Final answer:
Equation (C) f(x)=(x-1)²-9 already displays the minimum value of the function without any need for modification since it is in vertex form.
Step-by-step explanation:
The equation that reveals the minimum or maximum value of f(x) without changing the form of the equation is (C) f(x)=(x-1)²-9. This is because it is already in vertex form which is f(x) = a(x-h)²+k, where (h, k) is the vertex of the parabola. The coefficient a determines if the parabola opens upwards (a > 0) or downwards (a < 0), and thus whether it has a minimum (a > 0) or maximum (a < 0). In this case, with a=1 (since it’s not shown it’s understood to be 1), the parabola opens upwards, so the vertex (-1, -9) gives the minimum value of the function.
Equations (A), (B), and (D) are not in vertex form, but can be converted to find the minimum or maximum. For example, equation (B) f(x)=x²+2x-4x-8 can be simplified to f(x)=x²-2x-8 and then completed to square form to find the vertex thus the minimum or maximum.