Transformation + root of a quadratic.

[zaddyzad]

Homework Statement

2sqrt (x^2-2), sqrt (4(x^2-2)), x^2.

The first 2 formulas are the same thing. However I want to how I would explain the transformation of x^2 to either or of those. I have tried a myriad of things to try get x^2 to any of those other two graphs. A quick answer would be appreciated.

Homework Equations

The Attempt at a Solution

 

[zaddyzad]

for a test a tomorrow. Only thing I don't really get quadratic + root + transformation.

How would I write X^2-9 rooted then stretched horizontally by a factor of 4 and y by a factor of 2 then right 2 and down 1.

I will understand the idea if someone just solves this for me.

 

[HallsofIvy]

Homework Statement

2sqrt (x^2-2), sqrt (4(x^2-2)), x^2.

The first 2 formulas are the same thing. However I want to how I would explain the transformation of x^2 to either or of those. I have tried a myriad of things to try get x^2 to any of those other two graphs. A quick answer would be appreciated.

Homework Equations

The Attempt at a Solution

I) Subtract 2 from y= x^2. Since that is a change in y, it moves the graph down two positions vertically.

II) Multiply that by 4. That "stretches" the graph vertically, by a factor of 4.

III) Take the square root. That will be a much more complicted change graphically, "stretching" vertically as long as 4(x^2- 2)< 1, "contracting" if 4(x^2- 2)> 1, with the amount of "stretch" or "contraction" depending upon x.