# Question #9728b

Mar 30, 2017

$f \left(x\right) = - 3 {x}^{2} - 12 x - 6$

#### Explanation:

Standard form of a parabola is $f \left(x\right) = a {x}^{2} + b x + c$.

First, let's distribute out ${\left(x + 2\right)}^{2}$.

${\left(x + 2\right)}^{2}$

$\left(x + 2\right) \left(x + 2\right)$

$\left(x \cdot x + 2 \cdot x + 2 \cdot x + 2 \cdot 2\right)$

${x}^{2} + 4 x + 4$

Now, plug this in to the equation and simplify.

$- 3 {\left(x + 2\right)}^{2} + 6$

$- 3 \left({x}^{2} + 4 x + 4\right) + 6$

$- 3 {x}^{2} - 12 x - 12 + 6$

$- 3 {x}^{2} - 12 x - 6$