Question

The path of a firework is described by the function: h(1) = 4.97? + 491 + 1.5
where h(t) is the height of the firework, in meters, and t is the time in seconds since the launch.
Determine the maximum height of the firework. Show work

Answer 1

To find the maximum height of the firework, we need to find the vertex of the function.
The vertex of the function h(t) = a(t-b)^2 + c is (b,c), where b is the x-coordinate of the vertex, and c is the y-coordinate of the vertex.
In this case, h(1) = 4.97(1)^2 + 491(1) + 1.5 = 497.47 meters.
So, the vertex is (1, 497.47).
Therefore, the maximum height of the firework is 497.47 meters.