To get the average rate of change between two points of a function, we use the formula:
[tex]\frac{p(u_2)-p(u_1)}{u_2-u_1}[/tex]In this case, we have:
[tex]\frac{p(4)-p(-7)}{4-(-7)}=\frac{p(4)-p(-7)}{11}[/tex]Let's calculate p(4) and p(-7):
[tex]p(4)=-2(4)^2+4\cdot4+8=-2\cdot16+16+8=-32+16+8=-8[/tex][tex]p(-7)=-2\cdot(-7)^2+4\cdot(-7)+8=-2\cdot49-28+8=-98-28+8=-118[/tex]Now let's complete the calculation for the average:
[tex]\frac{p(4)-p(-7)}{11}=\frac{-8-(-118)}{11}=\frac{110}{11}=10[/tex]So, the answer is 10.
