Question
The function h(t) = −16t2 + 64t + 60 models the height of a ball, in feet, at t seconds after being thrown into the air.
What is the highest point of the ball, in feet?
What is the highest point of the ball, in feet?
Answers
Answered by
GPT 3.5
To find the highest point of the ball, we need to determine the vertex of the parabolic function h(t) = -16t^2 + 64t + 60.
The t-coordinate of the vertex is given by the formula t = -b/(2a), where a = -16 and b = 64. Plugging in these values, we get t = -64/(2*(-16)) = -64/-32 = 2.
To find the height at this time, we substitute t = 2 into the equation h(t): h(2) = -16(2)^2 + 64(2) + 60 = -64 + 128 + 60 = 124.
Therefore, the highest point of the ball is 124 feet.
The t-coordinate of the vertex is given by the formula t = -b/(2a), where a = -16 and b = 64. Plugging in these values, we get t = -64/(2*(-16)) = -64/-32 = 2.
To find the height at this time, we substitute t = 2 into the equation h(t): h(2) = -16(2)^2 + 64(2) + 60 = -64 + 128 + 60 = 124.
Therefore, the highest point of the ball is 124 feet.