# Question b3dd8

Sep 21, 2015

You can do this by "completing the square".
$y = 1.2 {\left(x + \frac{5}{6}\right)}^{2} + \frac{49}{6}$

#### Explanation:

$y = 1.2 {x}^{2} + 2 x + 9$

First, transfer 9 to the other side of the equation.
$y - 9 = 1.2 {x}^{2} + 2 x$

Factor out the coefficient of ${x}^{2}$.
$y - 9 = 1.2 \left({x}^{2} + \frac{2 x}{1.2}\right)$
$y - 9 = 1.2 \left({x}^{2} + \frac{5}{3} x\right)$

Now, we will compute for the value that we can add to ${x}^{2} + \frac{5}{3} x$ to make it a perfect square. Divide the coefficient of $x$ by 2 and multiply it by itself.
5/3÷2=5/6#
$\left(\frac{5}{6}\right) \left(\frac{5}{6}\right) = \frac{25}{36}$

Add $\frac{25}{36}$ inside the parentheses. We must also add $1.2 \left(\frac{25}{36}\right)$ to the other side to maintain equality.
$y - 9 + 1.2 \left(\frac{25}{36}\right) = 1.2 \left({x}^{2} + \frac{5}{3} x + \frac{25}{36}\right)$
$y - 9 + \frac{5}{6} = 1.2 \left({x}^{2} + \frac{5}{3} x + \frac{25}{36}\right)$
$y - \frac{49}{6} = 1.2 \left({x}^{2} + \frac{5}{3} x + \frac{25}{36}\right)$

Factor out ${x}^{2} + \frac{5}{3} x + \frac{25}{36}$. We made this into a perfect square trinomial so it should be easy.
$y - \frac{49}{6} = 1.2 \left(x + \frac{5}{6}\right) \left(x + \frac{5}{6}\right)$
$y - \frac{49}{6} = 1.2 {\left(x + \frac{5}{6}\right)}^{2}$

Transfer $\frac{49}{6}$ to the other side of the equation then you're done.
$y = 1.2 {\left(x + \frac{5}{6}\right)}^{2} + \frac{49}{6}$