Height of a Rocket

An Axis of Symmetry Problem

The height of a rocket is given by the equation h(t) = -6t^2 + 12t + 48. In this equation, height, h, is in meters, and time, t, is the number of seconds after it has been launched.

After how many seconds will the rocket reach its maximum height? How high will the rocket travel?

What are you being asked to do in Question 1?After how many seconds will the rocket reach its maximum height?

In this question, you are finding the amount of time needed to reach the highest point of the graph.

In other words, find the axis of symmetry!

Axis of SymmetryThe formula is x = -b/2a

For this function, b = 12 and a = -6. Plug in and solve.

X = -12/(2*-6)

X = -12/-12

X = 1

In the context of this question, the rocket will reach its maximum height in 1 second…

WOW that is fast!

What are you being asked to do in Question 2?How high will the rocket travel?

In this question, you are finding the highest point of the graph.

In other words, after you find the axis of symmetry, plug in that answer for time and solve for the height!!

If x = 1, then

h(1) = -6*1^2 + 12*1 + 48

h(1) = -6 + 12 + 48

h(1) = 54

In the context of this problem, the rocket will reach a maximum height of 54 meters.

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