On a graph, the maximum value of a function is its greatest output, not the input where it occurs. A downward-opening quadratic reaches its greatest height at its vertex, the point where the curve turns. Read that point directly instead of redrawing the graph in Desmos. For a maximum value, take the vertical coordinate; the horizontal coordinate tells you where it happens.
Hints
- Hint 1
A downward-opening parabola forms a hill, so its vertex, the point where it turns, is its highest point. Where is that point on the given graph?
- Hint 2
At a point on the graph of , is the input and is the output. The maximum value asks for which coordinate of the highest point?
Step-by-step
Read the peak from the graph
Step 1Find the highest point
No Desmos needed. The graph already shows its highest point. The parabola opens downward, so its vertex, the point where it turns, is its highest point. So read the marked dot.
- Step 2
Take the output, not the input
The marked dot is at , so the input is and the output is . The question asks for the maximum value of , so take the output, not the input where the peak happens. The maximum value is . Choice C.