Question 217·Easy·Nonlinear Functions
The graph of quadratic function is shown.
Which choice is the maximum value of ?
For a quadratic graph, first decide whether it opens up or down. If it opens down, the maximum value is at the vertex; if it opens up, the minimum value is at the vertex. Then read the vertex directly from the graph and use its -coordinate as the requested maximum (or minimum).
Hints
Look for the highest point
On a downward-opening parabola, the highest point is the vertex.
Use the vertex coordinates
Read the vertex from the graph and focus on its -coordinate.
Match to an answer choice
The maximum value is a single number (the largest output), not an -value.
Desmos Guide
Read the vertex from the graph
From the graph, identify the vertex coordinates by finding the highest point.
Enter a matching vertex-form equation
In Desmos, type , replacing and with the vertex coordinates you read from the graph.
Confirm the maximum output
Because the coefficient is negative, the parabola opens downward, so the maximum value is the vertex’s -coordinate . Match that value to the answer choices.
Step-by-step Explanation
Locate the vertex (where the maximum occurs)
Because the parabola opens downward, the maximum value of occurs at the vertex. From the graph, the vertex is at .
Read the maximum value
The maximum value is the vertex’s -coordinate, so the maximum value of is (choice ).