In order to determine in which quadrant the vertex of the quadratic function is located, we need to find the coordinates of the vertex. The vertex of a quadratic function given in the form y = a(x - h)² + k is the point (h,k).
In our function y = -2(x - (5/2)) + 48, the "h" value inside the parentheses represents the x-coordinate of the vertex and the "k" value outside the parentheses represents the y-coordinate of the vertex.
By examining the function, we can see that h = 5/2 and k = 48. Therefore, the vertex of our quadratic function is at the point (5/2, 48).
To determine the quadrant, recall that in a coordinate plane:
1. Quadrant I is where both x and y are positive.
2. Quadrant II is where x is negative and y is positive.
3. Quadrant III is where both x and y are negative.
4. Quadrant IV is where x is positive and y is negative.
Given that both x and y of the vertex are positive, i.e., x = 5/2 and y = 48, it can be inferred that the vertex is in Quadrant I.
So, the correct answer is (A) Quadrant I.