A quadratic model with a negative coefficient on graphs as a hill. Its highest point is the vertex, or turning point. If the equation doesn't show that point directly, graph it in Desmos and click the peak. When the question asks how many units achieve the maximum, use the input coordinate, not the revenue in dollars.
Hints
- Hint 1
The input counts smartwatches, while the output counts dollars. Since the question asks how many smartwatches, which coordinate of a point on the graph should you report?
- Hint 2
The coefficient of is negative. A parabola, the graph of a quadratic, opens downward in that case. So its highest point is the one you need to locate.
- Hint 3
The vertex is the turning point of a parabola. Graph the revenue model in Desmos and click that point. Which coordinate measures smartwatches rather than dollars?
Step-by-step
Read the peak from the graph
Step 1Identify the coordinate you need
The input counts smartwatches, while counts dollars. So how many smartwatches asks for the input coordinate of the peak. At a maximum, “how many” means the input, not the output.
- Step 2
Determine whether the graph has a peak
In , the negative coefficient of makes the graph open downward. So its vertex, the turning point, is its highest point.
- Step 3
Find and interpret the vertex
Type into Desmos and click the peak. Desmos labels the vertex . The first coordinate counts smartwatches; the second is revenue in dollars. So the company must produce and sell smartwatches each day for maximum revenue. Choice B.