10.5 Graphing
Square Root
Functions
Algebra I
First, let’s look at the parent
graphs.
y x
4.5
4
16, 4
3.5
3
9, 3
2.5
2
4, 2
1.5
1
1, 1
0.5
0
0, 0
0
2
4
6
8
10
12
14
16
18
Now, what happens when there is a number
in front of the radical?
y2 x
12
10
25, 10
8
16, 8
6
9, 6
4
4, 4
2
1, 2
0
0, 0
0
5
10
15
20
25
* Notice the graph goes thru
the points (0,0) and (1,2).
30
Generalization
ya x
Always goes thru
the points (0,0) and
(1,a).
Ex. 1: Graph y  4
x
Goes thru the points (0,0) and (1,a).
Since a=-4, the graph will pass thru
(0,0) and (1,-4)
0
0, 0
0
5
10
15
20
25
30
1, -4
-5
-10
9, -12
-15
16, -16
-20
-25
25, -20
Now, what happens when there are
numbers added or subtracted inside and/or
outside the radical?
y  a xh k
Step 1: Find points on the parent graph
ya
x
Step 2: Shift these points h units horizontally (use
opposite sign) and k units vertically (use same
sign) or use t-chart to figure out 2 new points.
Ex. 2: Describe how to obtain the graph of
y  x  2  1 from the graph of y  3 x
3
Shift all the points from
To the right 2 and up 1.
y3 x
Ex. 3: Graph y  2 x  4  1
(x-value – 4)
(y-value -1)
table for y  2 x
x
0
Now, shift these points to the left 4
and down 1.
y
0
6
x
y
5
5, 5
4
1
2
-4
-1
3
0, 3
2
4
9
4
-3
1
6
0
3
5
5
-3, 1
1
0
-6
-4
-2
-4, -1
0
-1
-2
2
4
6
Ex. 3 & 4: State the domain and range of
the functions in the last example.
x-values
y  2 x  4 1
6
5
5, 5
4
3
0, 3
2
-3, 1
1
0
-6
-4
-2
0
-4, -1
2
4
-1
-2
Domain:
Range:
x  4
y  1
The graph has a beginning
point of (-4,-1).
6

Assignment