To determine the maximum height of the firework, we need to find the vertex (highest point) of the quadratic function.
The formula for the vertex of a quadratic function in standard form (ax^2 + bx + c) is:
x = -b/2a
y = f(x) = ax^2 + bx + c (plug in the value of x)
In this case, the function is already in standard form:
h(t) = -4.9t^2 + 49t + 1.5
a = -4.9, b = 49, c = 1.5
Using the formula for the vertex, we get:
t = -b/2a = -49/(2*(-4.9)) = 5
h(5) = -4.9(5)^2 + 49(5) + 1.5 = 122.5
Therefore, the maximum height of the firework is 122.5 meters.
The path of a firework is described by the function: h(t) = -4.9t^2+ 49t+ 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
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