1. Write the parabola in vertex form:

Warm-Up

Graphs of Radical & Cube Root Functions

Domain, Range, & Shifts

October 7th

Solving Square Root Functions

Solving Square Root Functions

A square root function is a function containing a square root with the independent variable in the radicand.

The easiest way to graph a function is to create an x and y table.

Graph y =

Graphing Square Root Functions

x y

0

1

2

4

9

xy

Can you take the square root of a negative number??? So … when you are graphing square roots there is no need for you to include negative x values in your table.

Remember taking the square root of a negative number creates no real roots, so you will be unable to graph non-real roots.

So to find what number to start with we need to find the x-value that will give you a real number answer

Set the radicand equal to zero. Solving will provide us with the start value.

For example what if we had

We would set x – 2 = 0 and solve for x.

Radicand

2 xy

To complete the x/y table, we need to decide where to start.

Set the RADICAND equal to 0. x + 7 = 0, Start with x = -7

Graphing Radical Functions

37 x

x

x

x

x

x

32

74

5

16

8

Determine the start values

3

93

093

93

x

x

x

x

Domain of a Radical Function

Given the Radicand:

Set up an inequality showing the radicand is greater than or equal to 0.

Solve for x.

The result is your DOMAIN!

x

x

x

x

x

32

74

5

16

8

Determine the DOMAIN

Domain: Domain:Range: Range:

Graph the function

x yx y

xx 8

Domain: Domain:Range: Range:

Graph the functionxx 2 4

x yx y

Domain: Domain:Range: Range:

Graph the functionxx

3

2 3

x yx y

Domain: Domain:Range: Range:

Graph the functionxx 3 5

x yx y

We are going to look back at the graphs we made and compare/contrast the similarities and differences among their graphs and functions.

Compare the graphs

Domain: Domain:Range: Range:

Graph the function

x yx y

xx 8

When you ADD or SUBTRACT under the radical, you shift in the opposite direction.

Graph the function

4xx y

4 0

5 1

8 2

13 3

20 4

x3

2 x y0 0

.5 1

2 2

4.5

3

8 4

x y0 0

1.5 1

3 2

13.5 3

24 4

When you DIVIDE or MULTIPLY under the radical, the graph is STRETCHED out side to side or COMPRESSED.

x2

When you ADD or SUBTRACT outside of the radical, you shift UP or DOWN.

Graph the function5 3 xx

x y0 -5

1 -4

4 -3

9 -2

16 -1

x y0 3

1 4

4 5

9 6

16 7

1. Subtract under the radical

2. Add under the radical

3. Multiply under the radical

4. Divide under the radical

5. Add outside of the radical

6. Subtract outside of the radical

a) Move upb) Move right

c) Move downd) Move lefte) Stretchf) Compress

Recap Radical Shifts Matching

Worksheet – Don’t do the top three on the back of the worksheet

Homework