Question

question 18 (5 points)

consider points a, b, and c in the graph. which point is the global maximum?

a) none of these
b) a
c) c
d) b

Explanation:

Identify the given points and graph features

Using the Parabola Features knowledge point
The graph displays a downward-opening parabola with its vertex located at approximately \((0.5, 2.25)\). Three specific points are labeled on the curve:

• Point \(a\) is located at the vertex of the parabola, which is the highest point on the entire graph.
• Point \(b\) is located on the right side of the vertex, at approximately \((1, 2)\).
• Point \(c\) is located on the left side of the vertex, at approximately \((-1.5, -2)\).

Define global maximum

Using the Relative Extrema knowledge point
A global maximum of a function is the point where the function reaches its absolute highest \(y\)-value over its entire domain. For a downward-opening parabola, the vertex represents both the local (relative) maximum and the global (absolute) maximum.

Determine the global maximum point

Comparing the \(y\)-coordinates of the labeled points:

• Point \(a\): \(y \approx 2.25\)
• Point \(b\): \(y \approx 2\)
• Point \(c\): \(y \approx -2\)

Since point \(a\) has the highest \(y\)-value on the entire graph, it is the global maximum.

Answer:

• A) None of these
• B) a (Correct answer)
• C) c
• D) b