# Question #9ce6a

May 29, 2017

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

#### Explanation:

See https://socratic.org/s/aF6V8h4L for another full explanation of method but with a different equation.

Given:$\text{ } y = - 2 {x}^{2} - 8 x - 13$

Write as:$\text{ } y = - 2 \left({x}^{2} + 4 x\right) + k - 13$

Note that $\left(- 2\right) \times \left(+ 4 x\right) = - 8 x$

Halve the $x$ term

$\text{ } y = - 2 \left({x}^{2} + 2 x\right) + k - 13$

Remove the $x$ from the $x$ term

$\text{ } y = - 2 \left({x}^{2} + 2\right) + k - 13$

Move the exponent (power) to outside the brackets.

$\text{ } y = \textcolor{red}{- 2} {\left(x \textcolor{m a \ge n t a}{+ 2}\right)}^{2} + k - 13$

Determine the value of $k$

Set $\left(\textcolor{red}{- 2}\right) \times {\left(\textcolor{m a \ge n t a}{+ 2}\right)}^{2} + k = 0$

$\implies - 8 + k = 0 \text{ "=>" } k = + 8$

$y = - 2 \left({x}^{2} + 2\right) + k - 13 \text{ "->" } y = - 2 \left({x}^{2} + 2\right) + 8 - 13$

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