Question

What is the average rate of change for this quadratic function for the interval

from x = 1 to x = 3?
O A. -8
B.-4
O O
C. 8
O D. 4

Answer 1

Answer: -4 (choice B)

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Step-by-step explanation:

The table says that when x = 1, the output is y = -2.

So the point (1, -2) is on the parabola.

The table also says that point (3, -10) is on the parabola. We're focusing on this because x = 3 is the other endpoint.

Find the slope of the line through those two points. The slope here is the same as the average rate of change.

m = (y2 - y1)/(x2 - x1)

m = (-10 - (-2))/(3 - 1)

m = (-10 + 2)/(3 - 1)

m = -8/2

m = -4 is the slope, and therefore, the average rate of change from x = 1 to x = 3.