#### Answer

6

#### Work Step by Step

y = $x^{2}$ + 2x between x = 1 and x = 3
To find the rate of change, you have to use the rate of change formula:
$\frac{f(b)-f(a)}{b-a}$
In this problem, the starting point is at 1 and the end point is 3. Therefore, a = 1 and b = 3.
Knowing this, you can plug these numbers back into the formula.
$\frac{(3^{2}+2\times3)-(1^{2}+2\times1)}{3-1}$
= $\frac{(9+6)-(1+2)}{2}$
= $\frac{15-3}{2}$
= $\frac{12}{2}$
= 6
Therefore, the rate of change equals 6.