A ball is launched straight upward from a platform, and its height , in feet, seconds after launch is modeled by
According to the model, how many seconds after launch does the ball reach its maximum height?
A squared-time height model is a quadratic function, so its graph is a parabola. A negative coefficient on the squared term makes the parabola open downward, with its greatest height at the vertex, the turning point. Graph the model in Desmos and click the top point. If the question asks when the maximum occurs, read the time, not the height or the landing time.
Hints
- Hint 1
A quadratic function has a squared input. The coefficient of is negative here, so the graph opens downward. Which point on that graph gives the greatest height?
- Hint 2
The vertex is the parabola’s turning point. In Desmos, replace the time variable with , then click the highest point on the graph. Which coordinate measures seconds?
Step-by-step
Graph the height and read the peak
Step 1Identify the point that answers the question
The coefficient of is negative, so the graph is a downward-opening parabola, the curve made by a quadratic function. Its highest point is the vertex, or turning point. You need the time at that point, not the height.
- Step 2
Read the time at the highest point
Type in Desmos, using for time because Desmos graphs against . Click the curve, then its highest marked point. Desmos shows : the horizontal coordinate is time in seconds, and the vertical coordinate is height in feet. To find when a maximum occurs, read the vertex’s horizontal coordinate. The ball reaches its maximum height seconds after launch. Choice B.