https://file.aiquickdraw.com/mathbot/file/1727278695587vgkytfvk.jpg

The graph shows the height of the rocket \( h \) (in feet) as a function of time \( t \) (in seconds). From the image, we can observe that the highest point on the graph corresponds to the coordinates \( (16, 4096) \), where the rocket reaches its maximum height of 4096 feet after 16 seconds.

Thus, **16 seconds** have gone by when the rocket is at its highest point.

Would you like more details on how this type of problem is solved or have any questions?

Here are 5 related questions to expand your understanding:
1. How do we determine the time of maximum height in a general quadratic function?
2. What role does the vertex of a parabola play in projectile motion problems?
3. How would you model this rocket's motion using a quadratic equation?
4. What is the significance of the roots (32, 0) and (0, 0) in this context?
5. How can we use calculus to find the maximum height of a projectile?

**Tip:** In projectile motion, the highest point is always located at the vertex of the parabola.

A rocket is launched in the air. The graph below shows the height of the rocket h in feet after t seconds. How many seconds have gone by when the rocket is at its highest point?

Solve a real-world problem by determining the time at which a rocket reaches its maximum height. Using the quadratic function from the graph, students can learn about vertex properties in projectile motion. This example is suitable for students in Grades 8-10.

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