Download presentation
Presentation is loading. Please wait.
Published byAmi Ellis Modified over 9 years ago
1
For Educational Use Only © 2010 12.1 Functions Involving Square Roots Brian Preston Algebra 1 2009-2010
2
For Educational Use Only © 2010 Real World Application What is the biggest pendulum you have seen?
3
For Educational Use Only © 2010 Lesson Objectives 1) Evaluate and graph a function involving square roots. 2) Use functions involving square roots to model real-life problems, such as the length of a cycle of a pendulum.
4
For Educational Use Only © 2010 Graph y = 2x + 1 -3 -2 -4 -5 -3 -2 -4 -5 1 2 3 4 5 23 4 5 1 +2 +1 (0,1) slope = 2 y-int = 1 1 1 Regular line Review
5
For Educational Use Only © 2010 -3 -5 3 5 1 3 1 7 5 9 New line y = ax 2 + bx + c (0,0) (1,1) (2,4) (3,9) (-1,1) (-2,4) (-3,9) y = x 2 1 Parabola line Review
6
For Educational Use Only © 2010 2 2 y =+ 3 x–(–2) Center -3 -3 1 3 5 1 3 -5 5 ( h, k ) –2 2 + Review
7
For Educational Use Only © 2010 y =+ k x – h a Graphing a Square Root a = The bigger a is the steeper the curved line is. The smaller a is the flatter the curve line is. (h,k) = Starting point (Center) k = Translates (shifts) up or down. a + k h k Definition
8
For Educational Use Only © 2010 y =+ k Can you take the square root of a negative number? Graphing a Square Root Definition x – h a -3 -2 -4 -5 -3 -2 -4 -5 1 2 3 4 5 23 4 5 1 X is negative Y is negative No
9
For Educational Use Only © 2010 y =+ k We only use the positive quadrants. Graphing a Square Root Definition x – h a 2 6 8 4 4 2 8 6
10
For Educational Use Only © 2010 y =+ k Square Root Graph. Graphing a Square Root Starting point (h,k) Definition x – h a
11
For Educational Use Only © 2010 y = Sketch the graph. Find the domain & range. Example 2 6 8 4 4 2 8 6 1) x Not the right form
12
For Educational Use Only © 2010 0 0 y =+ Sketch the graph. Find the domain & range. Example x – 0 2 6 8 4 4 2 8 6 Center ( h, k ) 0 0 0 1) 1 Normal
13
For Educational Use Only © 2010 y =+ 0 Sketch the graph. Find the domain & range. Example x – 0 Domain 1) How can you get an undefined answer or error? 1 0 or – 2 No negative radicals
14
For Educational Use Only © 2010 y =+ 0 Sketch the graph. Find the domain & range. Example x – 0 Domain x – 0 1) x – 0 ≥ 0 x ≥ 0 The smallest number the radical can become is 0. Range
15
For Educational Use Only © 2010 y =+ 0 Sketch the graph. Find the domain & range. Example x – 0 Domain 1) x – 0 ≥ 0 x ≥ 0 y =+ 0 0 This is the lowest y value. Range
16
For Educational Use Only © 2010 0 0 y =+ Sketch the graph. Find the domain & range. Example x – 0 Domain 1) x – 0 ≥ 0 x ≥ 0 Range y ≥ 0 y ≥ 0
17
For Educational Use Only © 2010 2) The period T (in seconds) of a pendulum is the time it takes for the pendulum to swing back and forth. The period is related to the length L (in inches) of the pendulum by the model T = 2π. Find the period of a pendulum with a length of eight inches. Give your answer to the nearest tenth. period eight period Real World Application 8 2π2π L 384 L = T
18
For Educational Use Only © 2010 8 How long is the pendulum period? Real World Application 2) 2π2π 384 = T 2π2π = T 0.20… 2π2π = T 0.144… 0.9 = T seconds
19
For Educational Use Only © 2010 Real World Application How long does it take a cycle of the pendulum to occur? 0.9 seconds
20
For Educational Use Only © 2010 y =– 1 Sketch the graph. Find the domain & range. Example 2 6 8 4 4 2 8 6 3) x Not the right form
21
For Educational Use Only © 2010 y =– 1 Sketch the graph. Find the domain & range. Example x – 0 2 6 8 4 4 2 8 6 – 1 Center ( h, k ) 0 0 – 1 3) 1 Normal
22
For Educational Use Only © 2010 y =– 1 Sketch the graph. Find the domain & range. Example x – 0 Domain x – 0 3) x – 0 ≥ 0 x ≥ 0 The smallest number the radical can become is 0. Range
23
For Educational Use Only © 2010 y =– 1 Sketch the graph. Find the domain & range. Example x – 0 Domain 3) x – 0 ≥ 0 x ≥ 0 y =– 1 0 This is the lowest y value. Range
24
For Educational Use Only © 2010 y =– 1 Sketch the graph. Find the domain & range. Example x – 0 Domain 3) x – 0 ≥ 0 x ≥ 0 Range y ≥ – 1 y ≥
25
For Educational Use Only © 2010 y =+ 4 Sketch the graph. Find the domain & range. Example 2 6 8 4 4 2 8 6 4) x Not the right form
26
For Educational Use Only © 2010 4 4 y =+ Sketch the graph. Find the domain & range. Example x – 0 2 6 8 4 4 2 8 6 Center ( h, k ) 0 0 4 4) 1 Normal
27
For Educational Use Only © 2010 y =+ 4 Sketch the graph. Find the domain & range. Example x – 0 Domain x – 0 4) x – 0 ≥ 0 x ≥ 0 The smallest number the radical can become is 0. Range
28
For Educational Use Only © 2010 y =+ 4 Sketch the graph. Find the domain & range. Example x – 0 Domain 4) x – 0 ≥ 0 x ≥ 0 y =+ 4 0 This is the lowest y value. Range
29
For Educational Use Only © 2010 4 4 y =+ Sketch the graph. Find the domain & range. Example x – 0 Domain 4) x – 0 ≥ 0 x ≥ 0 Range y ≥ 4 y ≥ 4
30
For Educational Use Only © 2010 0 0 y =+ Sketch the graph. Find the domain & range. Example x – 3 2 6 8 4 4 2 8 6 Center ( h, k ) 3 3 0 5) 1 Normal
31
For Educational Use Only © 2010 + 3 x – 3 y =+ 0 Sketch the graph. Find the domain & range. Example Domain 5) x – 3 ≥ 0 x ≥ 3 The smallest number the radical can become is 0. Range + 3
32
For Educational Use Only © 2010 0 0 y =+ Sketch the graph. Find the domain & range. Example x – 3 Domain 5) Range y ≥ 0 y ≥ 0 x – 3 ≥ 0 + 3 x ≥ 3
33
For Educational Use Only © 2010 1 y =+ Sketch the graph. Find the domain & range. Example x + 1 2 6 8 4 4 2 8 6 6) Wrong form or think the opposite sign.
34
For Educational Use Only © 2010 1 1 y =+ Sketch the graph. Find the domain & range. Example x–(–1) 2 6 8 4 4 2 8 6 Center ( h, k ) –1 1 6) 1 Normal
35
For Educational Use Only © 2010 – 1 x–(–1) y =+ 1 Sketch the graph. Find the domain & range. Example Domain 6) x–(–1) ≥ 0 x ≥ – 1 The smallest number the radical can become is 0. Range – 1
36
For Educational Use Only © 2010 1 1 y =+ Sketch the graph. Find the domain & range. Example Domain 6) Range y ≥ 1 y ≥ 1 – 1 x–(–1) ≥ 0 x ≥ – 1 x–(–1)
37
For Educational Use Only © 2010 y =+ 0 Sketch the graph. Find the domain & range. Example 2 6 8 4 4 2 8 6 7) x Not the right form 2
38
For Educational Use Only © 2010 0 0 y =+ Sketch the graph. Find the domain & range. Example x – 0 2 6 8 4 4 2 8 6 Center ( h, k ) 0 0 0 7) 2 Steeper curved line
39
For Educational Use Only © 2010 y =+ 0 Sketch the graph. Find the domain & range. Example x – 0 Domain x – 0 7) x – 0 ≥ 0 x ≥ 0 The smallest number the radical can become is 0. Range 2
40
For Educational Use Only © 2010 y =+ 0 Sketch the graph. Find the domain & range. Example x – 0 Domain 7) x – 0 ≥ 0 x ≥ 0 y =+ 0 0 This is the lowest y value. Range 2
41
For Educational Use Only © 2010 0 0 y =+ Sketch the graph. Find the domain & range. Example x – 0 Domain 7) x – 0 ≥ 0 x ≥ 0 Range y ≥ 0 y ≥ 0 2
42
For Educational Use Only © 2010 3 3 y =+ Sketch the graph. Find the domain & range. Example x – 4 2 6 8 4 4 2 8 6 Center ( h, k ) 4 4 3 8) 2 Steeper curved line
43
For Educational Use Only © 2010 + 4 x – 4 y =+ 3 Sketch the graph. Find the domain & range. Example Domain 8) The smallest number the radical can become is 0. Range 2 x – 4 ≥ 0 x ≥ 4 + 4
44
For Educational Use Only © 2010 3 3 y =+ Sketch the graph. Find the domain & range. Example Domain 8) Range y ≥ 3 y ≥ 3 x – 4 2 + 4 x – 4 ≥ 0 x ≥ 4 + 4
45
For Educational Use Only © 2010 9 9 y = Evaluate the function for the given value of x. Example 9) 3 9 x ; y = 3 x
46
For Educational Use Only © 2010 9 9 y = Evaluate the function for the given value of x. Example 9) 3 x ; y = 3 3 y = 3 y = 9
47
For Educational Use Only © 2010 – 2 x y = Evaluate the function for the given value of x. Example 10) (– 2) 21 – 2x ; y = 21 – 2 y = 21 y = + 4 = 5 25
48
For Educational Use Only © 2010 x y = Evaluate the function for the given value of x. Example 11) ( ) 36x – 2 ; y = 36 y = 18 y = – 2 = 4 16 – 2 1 2 1 2
49
For Educational Use Only © 2010 1) Don’t forget the negative signs. 2) Make sure you have the right center. Key Points & Don’t Forget y =+ k x – h a (h,k) not (– h,k) h
50
For Educational Use Only © 2010 pg. 496-497 #’s 18-42 even, 43-45, 52-64 even The Assignment
51
For Educational Use Only © 2010 Please email brianspowerpoints@gmail.com with errors, confusing slides, improvements, complications, or any other comments or questions.brianspowerpoints@gmail.com The template is from www.spiralgraphics.bizwww.spiralgraphics.biz http://www.worldofteaching.comhttp://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching. Bibliography
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.