A model rocket is launched. Its height above the ground, in meters, seconds after launch is modeled by
What is the maximum height, in meters, the rocket reaches?
A height model with a negative squared term graphs as a hill, so its vertex is the peak. If the equation doesn’t show that point directly, graph it in Desmos and click the highest point. For a maximum height, use the vertical coordinate; the horizontal coordinate tells when the peak happens.
Hints
- Hint 1
The sign of the squared term tells which way a parabola curves. A negative sign makes a hill rather than a valley. Where on that hill is the greatest height?
- Hint 2
A vertex is the point where the curve turns around. Desmos can mark it, but its coordinates have different jobs: time comes first, height second. Which one does the question ask for?
Step-by-step
Graph and read the peak
Step 1Identify the point you need
The coefficient of is negative, so the height graph curves downward. Its vertex, the turning point, is the peak. That’s the point to find for the rocket’s maximum height.
- Step 2
Choose the height coordinate
The input counts seconds, while the output counts meters of height. At the vertex, the horizontal coordinate tells when the peak occurs; the vertical coordinate gives the maximum height. So you’ll need the second coordinate, not the time.
- Step 3
Read the maximum from Desmos
Type , using for time because Desmos graphs functions against . Click the curve, then its highest marked point. Desmos shows : the rocket reaches its peak after seconds, and its maximum height is meters. Grid in 16.