Interpreting a quadratic in factored form

TL;DR

This video discusses the height of a rocket at different times after launch, including its initial height, the time it hits the ground, the time it reaches maximum height, and the maximum height it reaches.

Transcript

• [Instructor] We are told a rocket is launched from a platform. Its height in meters, x seconds after the launch is modeled by h of x is equal to negative four times x plus two times x minus 18. Now, the first thing they ask us is what is the height of the rocket at the time of launch? Pause the video and see if you can figure that out. Well, what... Read More

Key Insights

• 🚀 The height of the rocket at the time of launch is determined by substituting x=0 into the height function.
• 😫 To find the time when the rocket hits the ground, the height function is set equal to zero and solved for x.
• ☺️ The maximum height of the rocket is found by averaging the x-values where the height function is equal to zero.

Questions & Answers

Q: What is the height of the rocket at the time of launch?

The height of the rocket at the time of launch is -18 meters. This is determined by substituting x=0 into the given expression for the rocket's height.

Q: How many seconds after launch will the rocket hit the ground?

The rocket hits the ground 18 seconds after being launched. This is found by setting the height function equal to zero and solving for x.

Q: How many seconds after being launched will the rocket reach its maximum height?

The rocket reaches its maximum height 8 seconds after being launched. This is obtained by averaging the two x-values where the height function is equal to zero, which are x=18 and x=-2.

Q: What is the maximum height that the rocket will reach?

The maximum height the rocket will reach is 400 meters. This height is determined by evaluating the height function at x=8, which is the time when the rocket reaches its maximum height.

Summary & Key Takeaways

• The height of the rocket at the time of launch is -18 meters.

• The rocket hits the ground 18 seconds after being launched.

• The rocket reaches its maximum height 8 seconds after being launched.