Final answer:
The height of the platform from which the circus acrobat jumps is determined by evaluating the quadratic equation h=-0.5d^2+0.5d+6 at d=0, yielding a height of 6 meters.
Step-by-step explanation:
The student's question revolves around deriving the height of a platform from a given quadratic equation that models the vertical motion of an acrobat jumping off the platform and landing on a trampoline. Let's analyze the provided equation: h = -0.5d^2 + 0.5d + 6, where h is the height above the stage and d is the horizontal distance from the edge of the platform.
To find the height of the platform, we need to evaluate the equation when the horizontal distance d is zero, since this corresponds to the point where the acrobat is directly above the edge of the platform and just beginning the jump. By plugging d = 0 into the equation, we obtain h = -0.5(0)^2 + 0.5(0) + 6, which simplifies to h = 6 meters. Thus, the height of the platform is 6 meters.