Let's analyze the given function $g(x)$ using the provided forms.

1. Forms of the Function: $g(x) = 2(x - 4)^2 + 2$ $g(x) = 2x^2 - 16x + 30$ $g(x) = 2(x - 3)(x - 5)$

2. Key Characteristics:

   • Y-intercept: The y-intercept occurs when $x = 0$. Using the second form $g(x) = 2x^2 - 16x + 30$, substitute $x = 0$: $g(0) = 2(0)^2 - 16(0) + 30 = 30$ So, the y-intercept is $(0, 30)$.

   • Minimum Value: The first form ( g(x) = 2(x -