In the function y=-1/2(x-1)^2+3 what effect does the negative sign have

The effect of the negative sign is that it reflects the graph of the function over the x-axis.That means that the graph that represents such function is a parabola that opens downward, being its vertex the maximum of the graph.

Explanation:

The vertex form of a parabola is y = A (x - h)² + k.

The values of A, h, and k means the following:

A > 0 the parabola opens upward and the vertex is a minimum,A < 0 the parabola opens downward and the vertex is a maximum.A cannot be equal to zero.| A | > 0 the parabola is stretched vertically.| A | < 0 the parabola is compressed vertically. The vertex of the function is the point (h, k).

So, for the given function you have:

A = - 1/2, so the parabola opens downward and the vertex is the maximum.Also, since |A| < 1 means that the parabola is compressed vertically.The vertex is (1, 3), so the maximum of the function is 3 and it happens at x = 1.