Final answer:
The equation of the bridge's arch represents a downward-opening parabola with the vertex at (100, 20). The parabola does not have x-intercepts as they are complex, and the maximum height of the arch is 20 meters.
Step-by-step explanation:
The equation given for the bridge's arch is h = -\frac{1}{500}(x - 100)^2 + 20. This is a quadratic equation that represents a parabola. The general form of a quadratic equation is y = ax^2 + bx + c, where the vertex of the parabola is at the point (-b/2a, c) when a is not zero.
Turning point coordinates: The turning point, also known as the vertex of the parabola, can be found by completing the square or by using the vertex formula, (-b/2a, c). In this case, the a coefficient is -1/500, and the h coordinate is +20. The turning point is at (100, 20).
X-intercepts: To find the x-intercepts, we set h = 0 and solve for x. The quadratic formula can be used here, which results in x = 100 ± √(20 × 500), yielding two intercepts. However, these are complex, so the parabola does not actually cross the x-axis.
Sketch of the graph: The graph of this equation is a parabola opening downwards, with the vertex at (100, 20). The span of the arch and the maximum height are already given by the equation, so plotting these values and sketching the shape will provide the rough sketch of the arch.
The span of the arch is the distance between the two x-intercepts, which in this case does not apply since the arch does not cross the horizontal axis.
The maximum height of the arch is given directly by the h coordinate of the vertex, which is 20 meters.