# How do you find the first three iterate of the function f(x)=2x^2-5 for the given initial value x_0=-1?

Jan 6, 2018

$- 3 , 13 , 333$

#### Explanation:

$\text{substitute each previous iterate into } f \left(x\right)$

$f \left({x}_{1}\right) = 2 {x}_{0}^{2} - 5 = 2 {\left(- 1\right)}^{2} - 5 = - 3$

$f \left({x}_{2}\right) = 2 {x}_{1}^{2} - 5 = 2 {\left(- 3\right)}^{2} - 5 = 13$

$f \left({x}_{3}\right) = 2 {x}_{2}^{2} - 5 = 2 {\left(13\right)}^{2} - 5 = 333$