1. 4 minutes
Warm-Up
Identify each transformation of the parent function f(x) = x2.
1) f(x) = x2 + 5
2) f(x) = (x + 5)2
3) f(x) = 5x2
4) f(x) = -5x2
5) f(x) = (5x)2 6)

2. 8.6 Radical Expressions and Radical Functions
Objectives:
-Analyze the graphs of radical functions, and evaluate radical expressions
-Find the inverse of a quadratic function

3. Square-Root Functions
Can x be negative?
domain:
Can f(x) be negative?
range:

4. Example 1
Find the domain of
The domain of is

5. Transformations,
Vertical stretch or compression by a factor of ; for a < 0, the graph is a reflection across the x-axis.
Vertical translation k units up for k > 0 and units down for k < 0.
Horizontal stretch or compression by a factor of ; for b < 0, the graph is a reflection across the y-axis.
Horizontal translation h units to the right for h > 0 and units to the left for h < 0.

6.  Example 2 Describe the transformations applied to . y = –21 2 
Reflect across the x-axis.
Stretch vertically by factor of 2.
Stretch horizontally by factor of 2.
Translate horizontally 1 unit right.
Translate vertically 1 unit down.

7. Example 3
Find the inverse of y = 2x2 – 6. Then graph the function and its inverse together.
y = 2x2 – 6
Exchange x and y:
x = 2y2 – 6
Write as a quadratic equation in terms of y
2y2 – 6 – x = 0
Solve for y:

8. Example 3
Find the inverse of y = 2x2 – 6. Then graph the function and its inverse together.

9. Example 4
You can use the formula to approximate the maximum distance, D, in miles that you can see from a height, x, in feet. Find the maximum distance you can see from heights of 10 feet, 20 feet, and 30 feet.

10. Cube-Root Functions Can x be negative? domain: Can f(x) be negative?
range:

11. Example 5
Evaluate each expression. a) b)

12. Practice
Evaluate the expression

13. Practice
Find the domain of the function

14. Homework
p.525 #11,15,17,23,25,29,33,37,41,45,57,61