# Question #bc809

Sep 12, 2016

$3 f \left(2 x\right) = 3 \left(8 {x}^{2} - 6 x + 1\right) = 24 {x}^{2} - 18 x + 3$.

#### Explanation:

Given: $f \left(x\right) = 2 {x}^{2} - 3 x + 1$, to find $3 f \left(2 x\right) \text{, or, in fact, } f \left(2 x\right)$,

what we have to do is : simply replace $x$, in the formula given for

$f \left(x\right)$, by $2 x$, as shown below :

$f \left(x\right) = 2 {x}^{2} - 3 x + 1 \Rightarrow f \left(2 x\right) = 2 {\left(2 x\right)}^{2} - 3 \left(2 x\right) + 1$

$= 2 \left(4 {x}^{2}\right) - 6 x + 1 = 8 {x}^{2} - 6 x + 1$.

$\text{ Therefore, } 3 f \left(2 x\right) = 3 \left(8 {x}^{2} - 6 x + 1\right) = 24 {x}^{2} - 18 x + 3$.