the maximum height is reached at \( t = 1 \) second, and the maximum height is \( 20 \) meters.
The given function \( h(t) = -5t^2 + 10t + 15 \) represents the height of the ball above the ground, in meters, at time \( t \) seconds after it is thrown. Let's analyze the function:
1. The coefficient of the \( t^2 \) term (\(-5\)) indicates that the ball is subject to a downward acceleration due to gravity.
2. The coefficient of the \( t \) term (\(10\)) represents the initial upward velocity of the ball.
3. The constant term (\(15\)) is the initial height of the ball above the ground when \( t = 0 \).
The function is a quadratic equation, and the graph of \( h(t) \) represents a downward-opening parabola. The vertex form of the quadratic function is given by:
\[ h(t) = a(t - h)^2 + k \]
where \( (h, k) \) is the vertex of the parabola. For the given function:
\[ h(t) = -5(t - 1)^2 + 20 \]
This indicates that the maximum height is reached at \( t = 1 \) second, and the maximum height is \( 20 \) meters.
The probable question may be:
A ball is thrown upward from the ground. The height of he ball above the ground, in meters, t seconds after it is hrown is given by the function h(t) = -5t² + 10t + 15. Find the maximum height?