Question

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7. My equation is f(x)=2(x-9)^2+17

Answer 1

so the average rate of change between two points of a function is the slope between the two points.
Remember slope is:\[\frac{ \Delta y }{ \Delta x }\]
(change in y over change in x)
which can be written as:\[\frac{ y_{2}-y _{1} }{ x _{2}-x _{1} }\]
in this case:\[x_{2}=7\]
and \[x _{1}=4\]
To find the y-coordinates plug in the x values into f(x) so:\[y _{2}=2(7-9)^2+1\]
\[y _{1}=2(4-9)^2+1\]
Now just simplify those and plug them into the slope formula to find the average rate of change.

Answer 2

oh actualy those ones are 17s right?

Answer 3

sorry replace those +1s with +17s

Answer 4

im so confused
my euqation was
f(x)=2(x-7)^2+17