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

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

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Answer 1 · 2018-02-21T01:55:07

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, ${(- x - 2)}^{2} \to (- x - 2) (- x - 2) \to x^{2} + 2 x + 2 x + 4$ $(-x-2)^2->(-x-2)(-x-2)->x^2+2x+2x+4$

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

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

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

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

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

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

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Explanation:

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