The average rate of change of function is given by the formula,
[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]
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:
[tex]\begin{gathered} A(x)=\frac{\lbrack-(6)^2+3(6)-5\rbrack-\lbrack-(-2)^2+3(-2)-5\rbrack}{6-(-2)} \\ A(x)=\frac{\lbrack-36+18-5\rbrack-\lbrack-4-6-5\rbrack}{6+2} \\ A(x)=\frac{\lbrack-23\rbrack-\lbrack-15\rbrack}{8} \\ A(x)=\frac{-23+15}{8} \\ A(x)=\frac{-8}{8} \\ A(x)=-1 \end{gathered}[/tex]Answer-1
