1. Chapter 5.8 Radical Equations & Inequalities Standard & Honors
Algebra II Mr. Gilbert
Chapter 5.8 Radical Equations & Inequalities
Standard & Honors
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2. Agenda Warm-up (next slide) Return Class work Lesson Homework
Check your answers
Return Class work
Lesson
Homework
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3. Class Work: Warm-up 7.9 (5 min.)
Solve:
2h4 – h3 +h2 +h – 3
h2-1
Find the third term of (x+y)34
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4. Class Work: Warm-up 7.9 (5 min.)
Solve:
2h4 – h3 +h2 +h – 3
h2-1 = 2h2 –h +3
Find the third term of (x+y)34
= 561 x32y2
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5. 7.9 Square Root Functions and Inequalities
Example 1 Graph a Square Root Function (4)
Example 2 Solve a Square Root Problem (4)
Example 3 Graph a Square Root Inequality (7)
You will need a graphing calculator
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Lesson 9 Contents

6. Real World
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7. Graph State the domain, range, and x- and y-intercepts.
Graph a Square Root Function
Graph State the domain, range, and x- and y-intercepts.
Since the radicand cannot be negative, identify the domain.
Write the expression inside the radicand as  0.
Solve for x.
The x-intercept is
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Example 9-1a

8. Make a table of values to graph the function.
Graph a Square Root Function cont.
Make a table of values to graph the function.
2.83 6
2.55 5
2.23 4
1.87 3
1.14 2
0.71 1 y x
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Example 9-1b

9. Graph a Square Root Function Cont.
Answer:
From the graph, you can see that the domain is and the range is y  0. The x-intercept is There is no y-intercept.
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Example 9-1c

10. x-intercept: 1 y-intercept: none
Graph State the domain, range, and x- and y-intercepts.
Answer:
domain: x  1
range: y  0
x-intercept: 1
y-intercept: none
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Example 9-1d

11. Graph the function. State the domain and range.
Solve a Square Root Problem
Physics When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object are related by the function
Graph the function. State the domain and range.
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Example 9-2a

12. The function is Make a table of values and graph the function.
Solve a Square Root Problem cont.
The function is Make a table of values and graph the function.
Answer:
The domain is a  0 and the range is v  0. a v 1
1.41 2 3
2.45 4
2.83 5
3.16
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Example 9-2b

13. Solve a Square Root Problem cont.
What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second?
Original equation
Replace v with 4.
Square each side.
Divide each side by 2.
Answer: The centripetal acceleration would be 8 meters per second squared.
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Example 9-2c

14. a. Graph the function. State the domain and range.
Geometry The volume V and surface area A of a soap bubble are related by the function
a. Graph the function. State the domain and range.
Answer:
domain: A  0
range: V  0
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Example 9-2d

15. b. What would the surface area be if the volume were 94 cubic units?
Answer: 100 units2
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Example 9-2e

16. Graph a Square Root Inequality
Graph the related equation Since the boundary is not included, the graph should be dashed.
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Example 9-3a

17. The domain includes values for So the graph is to the right of
Select a point and test its ordered pair.
Test (0, 0).
false
Shade the region that does not include (0, 0).
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Example 9-3b

18. Graph the related equation
The domain includes values for Select a point and test its ordered pair.
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Example 9-3c

19. Shade the region that includes (4, 1).
Test (4, 1).
true
Shade the region that includes (4, 1).
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Example 9-3d

20. a. Graph
Answer:
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Example 9-3e

21. b. Graph
Answer:
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Example 9-3f

22. Homework Review
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23. Homework
See Syllabus 5.8
p. 266: 13 – 27 odd and 39.
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24. Homework - Honors See Syllabus 5.8 p. 266: 13 - 39 odd, 41-43
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