Question

PLS OH PLS HELPPP Let f(x)=x^2+2x+3 . What is the average rate of change for the quadratic function from x=−2 to x = 5?

Answer 1

We're trying to find the average rate of change, so the first thing to do would be to find the total change. If we plug in (-2) and (5) into the quadratic equation, we get...
3
and
38
So, the total change is simply the final value, 38, minus the starting value, 3

Answer 2

Now that we have the total change, we can calculate the average rate of change. From -2 to 5, x has to increase by 7. We know this because 5 - (-2) is equal to 5+2.
Now, of course, since the function isn't linear, sometimes it increases more quickly and sometimes it increases more slowly.
On average, though, we can find the rate of change from one point to another by dividing the change in y by the change in x. In this case, y goes up by 35 and x goes up by 7.
So, what do you think?