Final answer:
The platform is 6 meters high, the acrobat landed 1 meter from the edge, and his maximum height was 6.125 meters above the stage.
Step-by-step explanation:
The equation provided models the acrobat's height (h) above the stage in relation to the horizontal distance (d) from the edge of the platform. To find the answers to the questions:
a) The height of the platform:
When the horizontal distance (d) is 0, that is, when the acrobat is just at the edge of the platform, we can find the height of the platform by substituting d = 0 into the equation: h = -0.5(0)^2 + 0.5(0) + 6 = 6 meters.
b) How far from the edge of the platform did the acrobat land?
To find where the acrobat lands, we need to determine the value of d when h is 0. Setting the equation to zero and solving for d gives us two possible distances, but only the positive distance makes physical sense: d = 1 meter and d = -12 meters. Since negative distance is not physically meaningful in this context, the acrobat landed 1 meter from the edge of the platform.
c) What was the acrobat's maximum height above the stage?
The maximum height is found at the vertex of the parabola represented by the equation. The horizontal distance at the vertex can be found using d = -b/(2a), which in this case is d = -0.5/(2 * -0.5) = 0.5 meters. Substituting this value back into the equation we get the maximum height h = -0.5(0.5)^2 + 0.5(0.5) + 6 = 6.125 meters.