Question

These tables represent a quadratic function with a vertex at (0,-1) what is the average rate of change for the interval from x=8 to x=9

Answer 1

From the information given the quadratic function is of the form,

$y=a(x-b)^2+c$ which has vertex at $(b,c)$

Since the vertex is $(0,-1)$, $b=0,c=-1$.

Thus the quadratic equation is $y=ax^2-1$. Since $y=ax^2-1$ passes through $(1,-2), (2,-5),..$, the equation of the quadratic function is $y=-x^2-1$.

The rate of change in the interval $(8,9)$ is

$\frac{\Delta y}{\Delta x} =\frac{y(9)-y(8)}{9-8} \\ \frac{\Delta y}{\Delta x} =\frac{-9^2-1+8^2+1}{1} \\ \frac{\Delta y}{\Delta x} =-17$

Answer 2

The answer would be D,-17 and I also have apex to