These tables represents a quadratic function with a vertex at (0,3) what is the average rate of change for the interval from x=8 to x=9

There are a few ways to do it; the easiest is just to follow the pattern of taking away two from the average.The next lines of the table are 6 to 7  -137 to 8   -158 to 9   -17Answer: C. -17Let's find the equation and do it that way.We have a vertex at (0,3) so we can fill out the vertex form a bit.  In general for vertex (p,q) it'sy = a(x-p)^2+qWe havef(x) = ax^2 + 3f(1) = 2a+3 =2a = -1So we found our equation,y = -x^2 + 3Let's check it at x=5, y=-5^2+3=-25+3=-22, goodWe want the rate of change from 8 to 9, which is[tex]r = \dfrac{f(9)-f(8)}{9-8}=f(9)-f(8)=-9^2 - -8^2 = -17[/tex]Answer: -17 again, that checks