a rocket is launched at the top of a building. the height of the rocket (in meters) written in terms of time (seconds) can be modeled by h(t)=-4.9t^2+9.8t+73.5. what is the maximum height?
recall that the vertex of a parabola ax^2+bx+c is at x = -b/2a
To find the maximum height of the rocket, we need to determine the vertex of the quadratic equation representing its height. In this case, the equation representing the height of the rocket is given as h(t) = -4.9t^2 + 9.8t + 73.5.
The vertex of a quadratic equation in the form of h(t) = at^2 + bt + c can be found using the formula t = -b / (2a). In this case, a = -4.9 and b = 9.8.
t = -9.8 / (2 * -4.9) = -9.8 / -9.8 = 1
Now that we have the time coordinate for the vertex, we can substitute this value of t back into the equation to find the maximum height.
h(1) = -4.9(1)^2 + 9.8(1) + 73.5
= -4.9 + 9.8 + 73.5
= 78.4
Therefore, the maximum height of the rocket is 78.4 meters.