The height of a golf ball in meters can be described by the equation $h=-4.9 t^{2}+23.7 t$, where $t$ is the number of seconds after it was hit. Find the vertex of this parabola, rounding each coordinate to the nearest tenth. The vertex of this parabola is

Step 1 ：The height of a golf ball in meters can be described by the equation \(h=-4.9 t^{2}+23.7 t\), where \(t\) is the number of seconds after it was hit. We are asked to find the vertex of this parabola, rounding each coordinate to the nearest tenth.

Step 2 ：The vertex of a parabola given by the equation \(y = ax^2 + bx + c\) is at the point \(-\frac{b}{2a}, f(-\frac{b}{2a})\). In this case, \(a = -4.9\) and \(b = 23.7\).

Step 3 ：We can calculate the \(t\)-coordinate of the vertex as \(-\frac{b}{2a}\), and then substitute this value into the equation to find the \(h\)-coordinate.

Step 4 ：By substituting \(a = -4.9\) and \(b = 23.7\) into \(-\frac{b}{2a}\), we get \(t_{vertex} = 2.4183673469387754\).

Step 5 ：Substituting \(t_{vertex} = 2.4183673469387754\) into the equation \(h=-4.9 t^{2}+23.7 t\), we get \(h_{vertex} = 28.657653061224483\).

Step 6 ：Rounding to the nearest tenth, the \(t\)-coordinate of the vertex is approximately 2.4 seconds, and the \(h\)-coordinate of the vertex is approximately 28.7 meters.

Step 7 ：This means that the golf ball reaches its maximum height of 28.7 meters after 2.4 seconds.

Step 8 ：\(\boxed{\text{The vertex of the parabola is at the point }(2.4, 28.7)}\)