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:

$Avg_{}=\frac{f(b)-f(a)}{b-a}$

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:

$Avg=\frac{38-3}{5-(-2)}=\frac{35}{7}=5$

Answer:

5