1. 6.5 Graphing Square Root & Cube Root Functions
Algebra II

2. First, let’s look at the parent graphs.

3. Now, what happens when there is a number in front of the radical?
* Notice the graph goes thru the points (0,0) and (1,2).
* Notice the graph goes thru the points (-1, 3), (0,0), & (1,-3).

4. Generalization Always goes thru the points (0,0) and (1,a).
Always goes thru the points (-1,-a), (0,0), and (1,a).

5. Ex. 1: Graph Goes thru the points (0,0) and (1,a).
Since a=-4, the graph will pass thru (0,0) and (1,-4)

6. Now, what happens when there are numbers added or subtracted inside and/or outside the radical?
Step 1: Find points on the parent graph
Step 2: Shift these points h units horizontally (use opposite sign) and k units vertically (use same sign).

7. Ex. 2: Describe how to obtain the graph of from the graph of
Shift all the points from
To the right 2 and up 1.

8. Ex. 3: Graph Now, shift these points to the left 4 and down 1. x y 0 0
(x-value – 4)
(y-value -1)
Now, shift these points to the left 4 and down 1.
x y 2 4
x y

9. Ex. 4: Graph Now, shift these points to the right 3 and up 2. x y
(x-value + 3)
(y-value + 2)
Now, shift these points to the right 3 and up 2.
x y -2 -4
x y 4 2 -2

10. Ex. 3 & 4: State the domain and range of the functions in the last 2 examples.
x-values
y-values
Domain:
Range:
Domain:
Range:
The graph doesn’t have a beginning or ending point.
(Meaning all x & y-values are possible.)
The graph has a beginning point of (-4,-1).

11. Assignment