Final answer:
The question revolves around a quadratic equation modeling a Blue Bird's flight path. By analyzing the equation y = -x^2 + 20x - 64, certain characteristics of the flight such as maximum height and takeoff/landing points can be determined. This requires understanding parabolas, vertex calculation, and finding x-intercepts using the quadratic formula.
Step-by-step explanation:
The quadratic equation y = -x2 + 20x - 64 models the flight path of a Blue Bird. This type of equation represents a parabola, which in this context can describe the trajectory of the bird's flight. Quadratic equations take the general form ax2 + bx + c = 0, where a, b, and c are constants. The mentioned equation can be analyzed to determine various characteristics of the bird's flight such as its maximum height, the distance traveled, and its initial and final positions.
To understand the bird's flight path better, we can find the equation's vertex, which represents the highest point in the bird's trajectory. The vertex formula, given by (-b/2a, f(-b/2a)), can be used here. Considering the given equation, we have a = -1, b = 20, and c = -64, and the vertex would thus be at (10, 36), indicating the bird reaches its maximum height of 36 units at 10 units horizontally from the origin.
The x-intercepts or roots of the equation can be found using the quadratic formula, x = (-b ± √(b2 - 4ac)) / (2a). These x-intercepts represent where the bird begins its flight and where it lands on the horizontal plane — assuming the path intersects the x-axis. Additionally, the flight path can be graphed to visualize the trajectory of the bird.