# How do you find the average rate of change of y= -3(x-4)^2+3 over interval [-4,9]?

Nov 5, 2015

$9$

#### Explanation:

average rate of change : $\frac{f \left(b\right) - f \left(a\right)}{b - a}$

$b = 9$
$a = - 4$

$\frac{\left(- 3 {\left(9 - 4\right)}^{2} + 3\right) - \left(- 3 {\left(- 4 - 4\right)}^{2} + 3\right)}{9 - \left(- 4\right)}$

$\frac{\left(- 3 {\left(5\right)}^{2} + 3\right) - \left(- 3 {\left(- 8\right)}^{2} + 3\right)}{13}$

$\frac{\left(- 3 \left(25\right) + 3\right) - \left(- 3 \left(64\right) + 3\right)}{13}$

$\frac{\left(- 72\right) - \left(- 189\right)}{13}$

$9$