Question

What is the average rate of change from f(-2) to f(6)?f(x)=-x^2+3x-5Type the numerical value for your answer as a whole number, decimal or a fraction

Answer 1

The average rate of change of function is given by the formula,

`A(x)=(f(b)-f(a))/(b-a)`

Given,

b = 6

a = -2

Let's substitute into the formula and calculate the average rate of change of the quadratic from -2 to 6. Shown below:

`\begin{gathered} A(x)=(\lbrack-(6)^2+3(6)-5\rbrack-\lbrack-(-2)^2+3(-2)-5\rbrack)/(6-(-2)) \\ A(x)=(\lbrack-36+18-5\rbrack-\lbrack-4-6-5\rbrack)/(6+2) \\ A(x)=(\lbrack-23\rbrack-\lbrack-15\rbrack)/(8) \\ A(x)=(-23+15)/(8) \\ A(x)=(-8)/(8) \\ A(x)=-1 \end{gathered}`Answer-1