find the average rate of change of g(x)=-2x^2+4 between g(-1) and g(2)

Answer 1

The given function is g(x) = -2x² + 4

g(-1) = -2(-1)² + 4 = -2 + 4 = 2 => point (-1, 2)

g(2) = -2(2)² + 4 = -8 + 4 = -4 => point (2, -4)

The average rate of change describes how one number changes, on average, in relation to another. For our function, it is the slope of the line drawn between the two given points.

From (-1, 2) to (2, -4) gradient = ^{change in y} / _{change in x} = ^{(y2 - y1)} / _{(x2 - x1)} = ^{-4 - 2} / _{2 - -1} = ^-6 / ₃ = -2

Hence the average rate of change between g(-1) and g(2) is -2

You can double-check by using Desmos Graphing or similar to plot the function y = -2x² + 4 and the above points, and the straight line y = -2x which passes through these points.