Answer:
The average rate of change for this quadratic function is -2.
Explanation:
In this question, we have f(x) = y = x^{2} + 4x + 5.
Given a function y, the average rate of change S of y=f(x) in an interval [x_s, x_f] will be given by the following equation:
S = \frac{f(x_{f}) - f(x_s)}{x_f - x_s}
So, in your problem, f(x) = x^{2} + 4x + 5, x_{f} = -2 and x_{s} = -4.
Applying these informations to the equation S above, we have:
S = \frac{f(-2) - f(-4)}{-2-(-4)}
Where
f(-2) = (-2)^{2} + 4(-2) +5 = 4-8+5 = 9-8 = 1
f(-4) = (-4)^{2} + 4(-4) +5 = 16-16+5 = 5
So, the average rate of change S will be
S = \frac{1-5}{2} = -4