The graph of the quadratic function is shown.
Which choice gives the maximum value of ?
For a quadratic graph question asking for a maximum or minimum, first check whether the parabola opens up or down. Then focus only on the vertex: the extreme value is the vertex’s -coordinate (maximum if it opens down, minimum if it opens up).
Hints
Use the shape of the parabola
Decide whether the parabola opens upward or downward.
Look for an extreme point
For a downward-opening parabola, the maximum occurs at the highest point on the curve.
Read a coordinate
Use the grid to read the -coordinate of that highest point.
Desmos Guide
Enter points the parabola passes through
In Desmos, enter a few clear points on the parabola from the graph, such as , , and (you may also include ).
Fit a quadratic to the points
Use quadratic regression to model the curve (for example, put the points in a table and use a quadratic fit).
Find the maximum on the model
Click the vertex of the fitted parabola; the -coordinate shown there is the maximum value of .
Step-by-step Explanation
Locate where the maximum occurs
Because the parabola opens downward, its maximum value occurs at its highest point, the vertex.
Read the maximum value from the graph
From the graph, the vertex’s -coordinate is , so the maximum value of is .