MATH ASSIGNMENT - UNIT 3 Task 1: Imagine a scenario involving a bungee jumper leaping from a bridge, with the jumper's height above the river surface modeled by the equation h(t) = -0.5t2 + v0t + h0, where h is measured in meters, t is in seconds, v0 represents the jumper's initial velocity in meters per second, and h0 is the initial height above the river. Given v0 = 0 m/sec and h0 = 210 meters. h(t) = -0.5t2 + 0t + 210 (i) Based on this scenario, answer the following questions that are related to the mathematical understanding of the concept: (a) What is the domain and range of h(t)? What is the physical significance of domain and range in this scenario? This is a quadratic function because it is a polynomial function of degree two and its…show more content… In this scenario, the vertex represents the extreme point. In this case, the value of a, -0.5, is less than 0, so the parabola opens downward. This means the vertex is the highest point on the graph, or the maximum value. The vertex is at (h, k) point in the standard form of a quadratic function: f(x)= a(x-h)2 + k. The value of h= -b/2a, and the value of k=f(-b/2a). a= -0.5, b=0, c= 210 h= (-0/2(-0.5)) = 0 k= f(h)= H(0)= -0.5(0)2 + 0(0) + 210= 210 The vertex is at (0,210) (c) At what time does the bungee jumper reach maximum height and what is the maximum height? Explain using the formula and scenario. The bungee jumper reaches the maximum height at the vertex of the parabola. To get this value, we get h, the vertex of the quadratic function. h= -b/2a,h= (-0/2(-0.5)) = 0 This means the jumper reaches maximum height in =0 seconds. To find the maximum height, we must find the y-coordinate of the vertex of the parabola, k
