Final answer:
The vertex of the quadratic function y = (1/2)(x + 4)(x - 2) is found by averaging the roots for the x-value, which is (-1), and then substituting it back into the function to find the y-value (-4.5). The correct vertex is (-1, -4.5).
Step-by-step explanation:
To find the coordinate of the vertex of the quadratic function y = (1/2)(x + 4)(x - 2), we first need to find the x-value of the vertex. This will be the average of the x-values where the function crosses the x-axis (the roots).
The roots are x = -4 and x = 2, so the x-value of the vertex is (-4 + 2)/2 = -1. Now, we need to find the y-value by substituting x = -1 into the function:
y = (1/2)(-1 + 4)(-1 - 2) = (1/2)(3)(-3) = -4.5
Therefore, the coordinates of the vertex are (-1, -4.5). Since this pair is not listed in the options given, it's possible there is a typo in the question, or the answer choices provided are incorrect.