Question

which function has a maximum at (2, 0)?

Explanation:

Step1: Identify max at (2,0)

A maximum at (2, 0) means the parabola opens downward (since it has a maximum, not minimum) and its vertex (the highest point) is at the coordinate (2, 0), where it touches the x-axis at x=2, y=0.

Step2: Analyze each graph

• Yellow graph: Vertex is on the y-axis (x=0), not (2,0).
• Purple graph: Vertex is at (2, 0), opens downward, matches the requirement.
• Orange graph: Opens upward (has a minimum, not maximum).
• Teal graph: Vertex is not at (2,0), and crosses x-axis at non-2 points.

Answer:

The function represented by the purple graph (second option from left)