# How do you sketch the graph of y=(-x-2)^2 and describe the transformation?

Feb 21, 2018

First, you have to use Binomial Multiplication (FOIL)

#### Explanation:

That first step is crucial. Many people will just distribute the square across the expression inside the parenthesis, but that is incorrect.

So, ${\left(- x - 2\right)}^{2} \to \left(- x - 2\right) \left(- x - 2\right) \to {x}^{2} + 2 x + 2 x + 4$

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

This is a parabola that opens up. The x coordinate of the vertex of a parabola can be found by $\frac{- b}{2 a}$, so $\frac{- 4}{2 \cdot 1} = - 2$

To get the y coordinate for the vertex, plug the -2 into your equation:

${\left(- 2\right)}^{2} + 4 \left(- 2\right) + 4 \to 4 - 8 + 4 = 0$

So, the vertex is at (-2,0)