# What is the vertex form of y= 3x^2-30x-72 ?

Mar 27, 2016

$y = 3 {\left(x - 5\right)}^{2} - 147$

#### Explanation:

Given:$\text{ } y = 3 {x}^{2} - 30 x - 72$

Let $k$ be the correction canstant

Write as;$\text{ } y = 3 \left({x}^{\textcolor{m a \ge n t a}{2}} - \frac{30}{3} x\right) - 72 + k$

Move the power of $\textcolor{m a \ge n t a}{2}$ to outside the bracket

$y = 3 {\left(x - \frac{30}{3} \textcolor{g r e e n}{x}\right)}^{\textcolor{m a \ge n t a}{2}} - 72 + k$

Remove the $\textcolor{g r e e n}{x}$ from $\frac{30}{3} x$

$y = 3 {\left(x - \frac{30}{3}\right)}^{2} - 72 + k$

Apply $\frac{1}{2} \times \left(- \frac{30}{3}\right) = \frac{30}{6} = 5$

$y = 3 {\left(x - 5\right)}^{2} - 72 + k$

For the correction to work it has to be the case that

$\textcolor{red}{3} \times {\left(- 5\right)}^{2} + k = 0 \text{ "=>" } k = - 75$

$\textcolor{red}{\text{(do not forget to multiply by the value outside the brackets)}}$

$y = 3 {\left(x - 5\right)}^{2} - 72 - 75$

$y = 3 {\left(x - 5\right)}^{2} - 147$