Final answer:
The graph of the skier's height over time, based on the quadratic function h = -5t^2 + 10t + 3, is a downward-opening parabola with an initial height of 3 meters. To find the height at 1.5 seconds, substitute t = 1.5 into the equation yielding a height of 6.75 meters.
Step-by-step explanation:
The question relates to the graphing of a function representing a skier's height over time and calculating the skier's height at a specific time. According to the provided equation h = -5t^2 + 10t + 3, this is a quadratic function, where h represents the skier's height above ground in meters, and t is the time in seconds.
Rough Sketch of the Graph
To sketch the graph, we note that the y-intercept is the initial height of the skier, which occurs at t = 0; plugging this into the function gives us h = 3 meters. The graph of a quadratic function is a parabola opening downwards, as indicated by the negative coefficient of the t^2 term. The vertex of the parabola represents the maximum height reached by the skier.
Height at 1.5 seconds
To find the skier's height at t = 1.5 seconds, we substitute this value into the equation to get h = -5(1.5)^2 + 10(1.5) + 3. Simplifying, h = -5(2.25) + 15 + 3, which equals h = -11.25 + 15 + 3, so the height is 6.75 meters at 1.5 seconds.