Final answer:
To create a table of values, substitute different time values into the height equation. The graph can be created by plotting the time values and corresponding heights. The approximate maximum height can be found by calculating the vertex and evaluating the height equation at that point.
Step-by-step explanation:
To create a table of values for the height equation (h(t) = -4.9t² + 39.2t + 42.3), choose a range of time values and substitute them into the equation to calculate the corresponding heights. For example, if you choose t = 0, 1, 2, 3, 4 as time values:
t=0 => h(0) = -4.9(0)² + 39.2(0) + 42.3 = 42.3
t=1 => h(1) = -4.9(1)² + 39.2(1) + 42.3 = 76.6
t=2 => h(2) = -4.9(2)² + 39.2(2) + 42.3 = 76.1
t=3 => h(3) = -4.9(3)² + 39.2(3) + 42.3 = 67.2
t=4 => h(4) = -4.9(4)² + 39.2(4) + 42.3 = 54.3
To create a graph of the function, plot the time values on the x-axis and the corresponding heights on the y-axis. Connect the points with a smooth curve.
The approximate maximum height of the object can be determined by finding the vertex of the quadratic function. The vertex can be calculated using the formula t = -b / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = -4.9 and b = 39.2. Plugging in these values, we get t = -39.2 / (2 * -4.9) ≈ 4.00 seconds. Substitute this value of t into the height equation: h(4.00) = -4.9(4.00)² + 39.2(4.00) + 42.3 ≈ **78.4 meters**. Therefore, the approximate maximum height of the object is c) 78.4 meters.