An emergency flare is shot vertically into the air with a speed of 60m/s. It's height h metres after t seconds is given by the equation h=−5(t−6)2+180 What is the maximum height of the flare?
since the equation is written in vertex form, just read the maximum height from the equation.
To find the maximum height, we need to determine the vertex of the parabolic equation h = -5(t - 6)^2 + 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.
To find the maximum height of the flare, we need to determine the vertex of the quadratic equation h=-5(t-6)^2+180.
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.
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