analyze and sketch graph

Quote:

Originally Posted by leki07

y=2(x+3)2 -2

Y=2(x+3)squared minus two

I really need help

This is certainly a parabola.

The 2 in front of,
$y=2(x+3)^2-2$
Show how much the parabola opens down/up.

1)Since we are sketching the graph we do not care about the specific way it opens up. The only thing we care about whether it opens down or opens up. Since the number in front is positive it opens up (it has a 'u' shape).

2)See that number in the end (-2) it says the parabola is shifted down to units.

3)See that number in parantheses $(x-2)^2$ means the parabola is shifted to the right two units.

4)That means you are going to sketch $y=2x^2$ and shift it to the right 2 units and then down 2 units.

5)Here is how it looks like (red is first parabola and blue is after the transformations of 2 and 2).