To find the maximum height reached by the ball, we will analyze the given quadratic function $h(t) = -2t^2 + 12t + 2.3$, where $h(t)$ is the height of the ball in meters and $t$ is time in seconds.

Steps:

1. Identify the form of the quadratic equation: The equation is in the form $h(t) = at^2 + bt + c$, where $a = -2$, $b = 12$, and $c = 2.3$.

2. Find the time at which the maximum height occurs: For a quadratic equation $h(t) = at^2 + bt + c$, the time at which the maximum height occurs is given by the vertex formula: $t_{\text{max}} = \frac{-b}{2a}$ Substituting $a = -2$ and $b = 12$: $t_{\text{max}} = \frac{-12}{2(-2)} = \frac{-12}{-4} = 3 \, \text{seconds}.$

3. Calculate the maximum height: Substitute $t = 3$ into the original equation to find the height at this time: [ h(3) = -2(3)^2