Please help!!

The average rate of change is the change in rise over the change in run

$Average\;rate \; of \;change=\frac{0-4}{2-0}=-2$

So yes he is right.

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$f(x)=x^2-4x+6\\ f(x)-6=x^2-4x\\ f(x)-6+(\frac{-4}{2})^2=x^2-4x+(\frac{-4}{2})^2\\ f(x)-6+4=x^2-4x+4\\ f(x)-2=(x-2)^2\\ $

The vertex is the minimum and it is at (2,2)