Final answer:
The baseball is at a height of 2 feet at two different times due to the symmetric arc of its flight path, represented by the quadratic equation. These times are when the baseball is on the way up and on the way back down which can be found by solving the equation for t.
Step-by-step explanation:
The student's question is about finding the times when a baseball hit into the air is at a height of 2 feet, given the quadratic equation h = -16t² + 64t + 2. To find the times when the baseball is at 2 feet, we need to set the equation equal to 2 and solve for t. This can be done using a graphing calculator or algebraically. Since the coefficient of the t² term is negative, the graph of the equation is an upside-down parabola. This shape tells us that there are two points in time when the ball will be at 2 feet — once on the way up and once on the way down.
The times can be found by solving the equation 0 = -16t² + 64t. Factoring out the common term t, we get t(-16t + 64) = 0. The two solutions are t = 0 (when the ball is hit) and t = 4 (when the ball comes back down to a height of 2 feet). The reason there are two such times is that the quadratic equation represents the path of the baseball as a symmetric arc, reaching a peak height and then descending back down.