SOLUTION: Write an equation for a function that has a graph with the given circumstances - The shape of y=sqrt(x) but shifted left 6 units and down 5 units.

Algebra ->  Graphs -> SOLUTION: Write an equation for a function that has a graph with the given circumstances - The shape of y=sqrt(x) but shifted left 6 units and down 5 units.      Log On


   

Question 270204: Write an equation for a function that has a graph with the given circumstances
- The shape of y=sqrt(x) but shifted left 6 units and down 5 units.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!


I think this graph satisfied your requirements.

The original graph is the higher one.

The revised graph is the lower one.

They both have the same shape.

The graph has been shifted to the left 6 units and down 5 units.

The vertex of the original one is at (x,y) = (0,0).

The vertex of the revised one is at (x,y) = -6,5).

when x = 9 units to the right of the vertex in the original graph, then x = 9 and y = +/- 3 which means the spread is 6.

when x = 9 units to the right of the vertex in the revised graph, then x = 3 and y = -2 and -8 which means the spread is 6.

The graphs have the same shape and the shift is accurate in the direction requested.

The shift was accomplished by changing your equation from:

y = sqrt(x)

to:

(y+5) = sqrt(x+6)

I used the standard formula of:

(y-k) = +/- sqrt(x-h)

If I wanted to shift the y value down 5 units, then k must be equal to -5 making the expression (y-k) equal to (y-(-5)) equal to (y+5).

If I wanted to shift the x value to the left 6 units, then h must be equal to -6 making the expression (x-h) equal to (x-(-6)) equal to (x+6).

It works, but you need to play with the numbers to see why it works.

having some graphing software available help makes the process easier.

A pretty good one can be found here:

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

Enter "sqrt(x)" in the first box
Enter "-sqrt(x)" in the second box
Enter "sqrt(x+6)-5" in the third box
Enter "-sqrt(x+6)-5" in the fourth box

Do not enter the exclamation points. Those are just to delineate what you have to enter more clearly.

Left Click on the graph button.

You should see the graphs I just showed you.

play with the 6 and the 5 by changing the numbers and you'll see how the graph shifts left or right or up or down.