Question

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

Answer 1

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 `(-3, 5)` as our transformation showed. Then we form a parabola.

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

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

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