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 -13
7 to 8 -15
8 to 9 -17
Answer: C. -17
Let'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's
y = a(x-p)^2+q
We have
f(x) = ax^2 + 3
f(1) = 2
a+3 =2
a = -1
So we found our equation,
y = -x^2 + 3
Let's check it at x=5, y=-5^2+3=-25+3=-22, good
We 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
