# How do you write y=3(x-3)^2-12?

Jan 15, 2017

See full solution process below:

#### Explanation:

First, expand and square the term in parenthesis:

$y = 3 {\left(x - 3\right)}^{2} - 12$

$y = 3 \left(\textcolor{red}{x} - \textcolor{red}{3}\right) \left(\textcolor{b l u e}{x} - \textcolor{b l u e}{3}\right) - 12$

$y = 3 \left(\left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{3}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{3}\right)\right) - 12$

$y = 3 \left({x}^{2} - 3 x - 3 x + 9\right) - 12$

$y = \textcolor{red}{3} \left({x}^{2} - 6 x + 9\right) - 12$

We can now fully expand the term in parenthesis by multiplying each individual term within the parenthesis by $\textcolor{red}{3}$

$y = \left(\textcolor{red}{3} \times {x}^{2}\right) - \left(\textcolor{red}{3} \times 6 x\right) + \left(\textcolor{red}{3} \times 9\right) - 12$

$y = 3 {x}^{2} - 18 x + 27 - 12$

Lastly, we can combine the constants:

$y = 3 {x}^{2} - 18 x + 15$