Question

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

Answer 1

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, `(-x-2)^2->(-x-2)(-x-2)->x^2+2x+2x+4`

So, `x^2+4x+4`

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

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

`(-2)^2+4(-2)+4->4-8+4=0`

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