\( 8 f ( x ) = x ^ { 2 } - 8 x + 15 \)

To get a better grasp of the function \( f(x) \), let's first isolate it by dividing everything by 8, giving us \( f(x) = \frac{1}{8} (x^2 - 8x + 15) \). This quadratic can be factored, and you'll find that it represents a parabola opening upwards, with roots that can be solved using the quadratic formula or by factoring directly. This function can be utilized in various fields! For instance, in physics, you might model projectile motion with a similar quadratic function. In business, maximizing profit or minimizing costs often leads to quadratic equations, allowing you to find optimal points effectively using functions like \( f(x) \).