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

1 Answer
Shantelle
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):
enter image source here

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.

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