Answer:
- 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.
