Solved:
Answered by AI, Verified by Human Experts
Alex laughed a ball into air the height of the ball can be represented by the equation h=-8t +40t+5, where h is the height in units,and t is the time ,in seconds,after the ball was launched. Graph the equation frim t=0 to t=5 seconds.
Alex laughed a ball into air the height of the ball can be represented by the equation h=-8t +40t+5, where h is the height in units,and t is the time ,in seconds,after the ball was launched. Graph the equation frim t=0 to t=5 seconds.
Final Answer:The height of the ball, represented by the equationcan be graphed over the time intervalseconds. The graph will show the trajectory of the ball during this time frame.Explanation:The given equation for the height of the ball, is a quadratic function in the form, where a = -8, b = 40, and c = 5. The graph of a quadratic function is a parabola, and in this context, it represents the path of the ball as it travels through the air.To graph the equation over the specified time intervalseconds, we substitute values for t and calculate corresponding values for h. For example, whenwhen t = 1, substitute into the equation to find h = 37; when t = 2, h = 69, and so on until t = 5. These pairs of (t, h) values can then be plotted on a coordinate system to form the parabolic trajectory of the ball.The coefficient of t^2 being negative (-8) indicates that the parabola opens downward, reflecting the fact that the height of the ball decreases over time due to gravity. The coefficient of t (40) influences the steepness of the parabola, while the constant term (5) is the initial height when t = 0. The resulting graph provides a visual representation of the ball's height as it is launched and descends within the specified time frame....