# How do you sketch the graph of y=(x+3)^2+6 and describe the transformation?

Dec 17, 2017

Refer to the explanation.

#### Explanation:

First, let's look at the transformations of this equation.

When something is with the $x$, in this case $x + 3$, then you will do the opposite of what it says, because when you set $x + 3$ to equal to $0$, then you will get $- 3$, which is the opposite of $3$.

However, when something is "outside" the $x$, in this case $6$, then that applies to the y-values and it just does what it says. So the y-values would always add $6$.

Here is the graph (should be arrows at each end, just doesn't show):

As you can see, there is a point, or the vertex, is at $\left(- 3 , 5\right)$ as our transformation showed. Then we form a parabola.

When the coefficient of a quadratic equation is positive , (ex: ${x}^{2}$, $10 {x}^{2}$) then the parabola will face up .

When the coefficient is negative, (ex: $- {x}^{2}$, $- 10 {x}^{2}$), then the parabola will face down .

Our coefficient is just $x$, so that is positive, therefore the graph grows up.