The function \( g \) is given in three equivalent forms. Which form most quickly reveals the \( y \)-intercept? Choose 1 answer: (A) \( g(x)=\frac{1}{2}(x-12)(x-4) \) (B) \( g(x)=\frac{1}{2} x^{2}-8 x+24 \) (C) \( g(x)=\frac{1}{(x-8)^{2}} \). 8

The form that most quickly reveals the \( y \)-intercept is option (B) \( g(x)=\frac{1}{2} x^{2}-8 x+24 \). This is a standard quadratic formula where the \( y \)-intercept can be directly read as the constant term, which is 24 when \( x = 0 \). In contrast, option (A) reveals the y-intercept as well, but requires some multiplication of the terms, and option (C) is a rational function that does not easily showcase the intercept at \( x = 0 \), making (B) the most straightforward choice!