Sample Word Problem with a Quadratic Equation

Do you need an example of a word problem involving a quadratic equation?  You've found it.  More specifically, it's a function, typically covered in the second semester of Algebra 1:

A toy rocket is launched from the rooftop of a building. The rocket's height, h(t), is modeled by the equation h(t) = -16t² +80t + 96 after t seconds.

  1. How tall is the building?
  2. How long before the rocket hits the ground at the base of the building?
  3. How high will the rocket be 5 seconds after take off?
  4. At what time will the rocket be 160 feet above the ground?

The following video shows how to solve this quadratic equation word problem.  Note: At the end of the video, I mispoke.  I said that #4 only has one answer.  That is wrong -- #4 has two answers.

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Once you have your password, click here to read the final steps. 

For Teachers & Tutors

If you're a teacher or tutor, here are some questions you might ask your student(s) before presenting them with the problem:

  1. Have you ever been on the roof of a building? Tell me about it.
  2. Have you ever launched a toy rocket? Tell me about it.
  3. What do you think of when you hear the word “function”?
  4. Can you think of an example of an algebra function?

And here are some questions you might ask before having your student(s) solve the problem:

  1. Could you please read the first 2 sentences of the problem out loud?
  2. What are the two variables? [height and time]
  3. Which letters symbolize each variable? [height = h(t); time = t]
  4. In this problem, what are the units of measurement for height and time? [height: feet (see part 4); time: seconds]
  5. Which variable would you make the x-axis, and which would you make the y-axis? [x-axis: time; y-axis: height]
  6. Draw a coordinate system on which you can later graph the problem.
  7. Label h(t) and t.


Thanks for visiting Can Do Math.  I hope you've found this word problem with a quadratic equation to be useful!