h =−5(t−6)^2+180 now complete the square
5 (t-6)^2 = 180 - h
(t-6)^2 = (1/5) (180-h)
vertex at t = 6 and h = 180
5 (t-6)^2 = 180 - h
(t-6)^2 = (1/5) (180-h)
vertex at t = 6 and h = 180
The vertex form of a parabolic equation is given by h = a(t - h)^2 + k, where (h, k) represents the vertex.
By comparing this form with the given equation, we can see that a = -5, h = 6, and k = 180.
Since the parabola opens downward (due to the negative coefficient of t^2), the vertex represents the maximum point.
Therefore, the maximum height of the flare is equal to the y-coordinate of the vertex, which is k.
Hence, the maximum height of the flare is 180 meters.
The vertex of a quadratic equation in the form h = a(t - h)^2 + k is given by (h, k), where h is the x-coordinate and k is the y-coordinate of the vertex.
In this case, the equation already provided is in vertex form, so we can directly read the vertex coordinates from the equation.
Comparing the given equation with the vertex form, we can see that the vertex coordinates are (6, 180).
Therefore, the maximum height of the flare is 180 meters.