# How do you sketch the graph of y=(x+6)^2-2 and describe the transformation?

Mar 20, 2018

See explanation.

#### Explanation:

The graph of a function given in a form:

## $y = a {\left(x - p\right)}^{2} + q$

can be obtained from the graph of

## $y = a {x}^{2}$

by translating it by a vector vec(v)=[p;q]

In the given example we have:

$a = 1$, $p = - 6$ and $q = - 2$

So we have to translate $y = {x}^{2}$ by $\vec{v} = \left[- 6 , - 2\right]$

graph{(y-x^2)(y-(x+6)^2+2)=0 [-10, 10, -5, 5]}