# Math Help - Transformations of graphs!

1. ## Transformations of graphs!

The graph of $y=sqrt(3x-x^2)$ is given. Use transformations to create a function whose graph is as shown.

1.)

2. It looks like a reflection in the x axis (ie f(x)=-y) followed by vertical (1unit down) and horizontal (4 units back) shifts in the negative direction.

3. Originally Posted by VonNemo19
It looks like a reflection in the x axis followed by vertical (1unit down) and horizontal 4 units back) shifts in the negative direction.
I'm trying to find the equation but I keep getting the wrong answer.

Here's the answer if it helps. I just don't know how to get that answer.
1) y= -sqrt(-x^2-5x-4)-1

Help!

4. Originally Posted by yoman360
I'm trying to find the equation but I keep getting the wrong answer.

Here's the answer if it helps. I just don't know how to get that answer.
1) y= -sqrt(-x^2-5x-4)-1

Help!
If I had $y=\sqrt{x}$. To flip it through the x axis I'd tack on a negative like so

$y=-\sqrt{x}$

If I wanted to slide it to the left 4 units I'd add four to the variable like this

$y=-\sqrt{(x+4)}$

If I then wanted it to shift down a unit I'd add a constant (subtract in this case)

$y=-\sqrt{(x+4)}-1$

Get it?

5. Originally Posted by VonNemo19
If I had $y=\sqrt{x}$. To flip it through the x axis I'd tack on a negative like so

$y=-\sqrt{x}$

If I wanted to slide it to the left 4 units I'd add four to the variable like this

$y=-\sqrt{(x+4)}$

If I then wanted it to shift down a unit I'd add a constant (subtract in this case)

$y=-\sqrt{(x+4)}-1$

Get it?
Ok I get it now I'm gonna try and see if I can get the answer. I'll put a post to tell you if i get it right or not.

6. Originally Posted by yoman360
Ok I get it now I'm gonna try and see if I can get the answer. I'll put a post to tell you if i get it right or not.
Sounds like a plan.

7. Ah I didn't get it right
this is what i did!
$y= sqrt(3x-x^2)$
$y= sqrt(-(3x-x^2))$
$y= -(sqrt(-(3x-x^2)))$
$y= -(sqrt(-(3x-x^2+1)))-1$
My answer: $y= - sqrt(-3x+x^2+1) - 1$

correct answer: $y=-sqrt(-x^2-5x-4)-1$

what did I do incorrectly?

8. Originally Posted by yoman360
what did I do incorrectly?
Since you gave it the old college try I'll do it for you.

$y=-\sqrt{3(x+4)-(x+4)^2}-1$

9. Originally Posted by VonNemo19
Since you gave it the old college try I'll do it for you.

$y=-\sqrt{3(x+4)-(x+4)^2}-1$
Thanks! But I don't understand how you got that.

10. Originally Posted by yoman360
Thanks! But I don't understand how you got that.
To flip it, I tacked on the negative.

To slide to the left, i added 4 wherever i saw an x.

to slide it down, i subtracted 1 from everything.

11. Originally Posted by VonNemo19
To flip it, I tacked on the negative.

To slide to the left, i added 4 wherever i saw an x.

to slide it down, i subtracted 1 from everything.
Oh thanks thats why! I relected y axis then shifted to the left 1 then reflected x axis then shift down 1.

12. Originally Posted by yoman360
Thanks! But I don't understand how you got that.
First 'move' it back 4 units by using $(x+4)$ for $x$.

Flip it by multipling by $-1$.

'Move' it down by subtracting $1$.

13. Originally Posted by yoman360
Oh thanks.
You're welcome. You can click them buttons whenever you feel like it yoman.