Question

which point is the best approximation of the relative maximum of the polynomial function graphed below?
a. (-1.8, 24.5)
b. (-2.4, 25.6)
c. (-2.2, 25.3)
d. (-1.2, 24.2)

Explanation:

Step1: Analyze the x - coordinate of the relative maximum

Looking at the graph, the x - coordinate of the relative maximum is between - 2.5 and - 1.5.

Step2: Analyze the y - coordinate of the relative maximum

The y - coordinate of the relative maximum is between 24 and 26.

Step3: Check each option

• Option A: \(x=-1.8\) (a bit to the right of the center of the x - range for the maximum), \(y = 24.5\) (lower end of the y - range)
• Option B: \(x=-2.4\) (close to the left - end of the x - range), \(y = 25.6\) (higher end of the y - range)
• Option C: \(x=-2.2\) (more centered in the x - range \((-2.5,-1.5)\)), \(y = 25.3\) (more centered in the y - range \((24,26)\))
• Option D: \(x=-1.2\) (far to the right of the x - range for the maximum), \(y = 24.2\) (lower end of the y - range)

Answer:

C. \((-2.2,25.3)\)