Jesse throws a basketball such that its height is modelled by the function h(t) = −4.9(t – 1.5)^2 + 12.5, where h is the height in metres and t is time in seconds.
What is the maximum height of the ball?
To find the maximum height of the ball, we need to determine the vertex of the parabolic function. In this case, the vertex form of the equation for a parabola is:
y = a(x - h)^2 + k
where (h, k) represents the vertex.
Comparing the given function to the vertex form, we can deduce that:
-4.9(t – 1.5)^2 + 12.5 = y
From this equation, we can see that the vertex occurs when (t - 1.5) = 0, which implies t = 1.5.
To find the maximum height h(t), we substitute t = 1.5 into the equation:
h(1.5) = -4.9(1.5 - 1.5)^2 + 12.5
h(1.5) = -4.9(0)^2 + 12.5
h(1.5) = -4.9 * 0 + 12.5
h(1.5) = 12.5
Therefore, the maximum height of the ball is 12.5 meters.