Question

Please help me with this problem so that my son can understand better. Let f(x)=x^2 +2x+3.What is the average rate of change for the quadratic function from x=−2 to x = 5? Enter your answer in the box.

Answer 1

`f(x)=x^2+2x+3`

We can find the average rate of change using the following formula:

`Avg_{}=(f(b)-f(a))/(b-a)`

Where:

`\begin{gathered} a=-2 \\ b=5 \\ f(a)=f(-2)=(-2)^2+2(-2)+3=3 \\ f(b)=f(5)=(5)^2+2(5)+3=38 \end{gathered}`

Therefore:

`Avg=(38-3)/(5-(-2))=(35)/(7)=5`

Answer:

5