here is the notes for February 9,11, and 13
here is the notes for February 9,11, and 13 106-06
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This 5 page Class Notes was uploaded by Rebecca Favorit on Tuesday February 17, 2015. The Class Notes belongs to 106-06 at Washington State University taught by mindy morgan in Spring2015. Since its upload, it has received 52 views. For similar materials see College Algebra in Math at Washington State University.
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Date Created: 02/17/15
Notes for February 913 February 9 2015 Announcements 0 EampN 15 due Wednesday 0 EampN 16 due Friday 0 Math Club Wednesday 211 6pm 0 My Math Lab Hw 7 due Thursday 212 0 My Math Lab Hw 8 due Sunday 215 0 NO CLASS MONDAY Section 15 Transformation of Functions Vertical Transformations o The graph yCfxD is obtained from the graph of yfx by applying a vertical scale and shift Vertical Scaling 1 Vertical Expansion by a factor C when Cgt1 Vertical Compression 1 By a factor C when OltClt1 Reference Line xaxis y0 Clt09vertical reflection across the reference line Note if shifting first yD Vertical Shift D units up if DgtO D units down if DltO Note it s a good idea to scale and reflect before shifting so that you don t have to change reference line Example a fxx gx2x59 which equals 2fx5 C2 and D5 o Gx is obtained b Vertical Reflection 0 During a vertical reflection it is always over the xaxis making the y coordinate its reciprocal pair For example 2 5 would change to 25 In this case the xcoordinate will stay the same February 11 2015 Section 15 Continued Horizontal Transformations Affects the xcoordinate YfAxB 0 Horizontal Expansion 0 By a factor of 1 divided by absolute vale of A if OltAlt1 o HorizontalCompression o By factor of A if Agt1 0 Horizontal Reflection Across o Yaxis or x0 if AltO Reference Line o B unit right if BgtO o B units left if BltO o Combining Transformations o YCfAxBD This is the formula that you are to have to remember during these kind of problems Section 16 Quadratic Functions 0 Standard Form 0 Fxaxquot2bxc A does NOT equal 0 I Graph is a parabola I AgtO opens upward I AltO opens downwards I Vertex is at the bottom of parabola I C will give you the yintercept where x090c This is what the intercept coordinate looks like 0 Transformation Form 0 Gxaxhquot2k I Vertical expansioncompression by a factor of a if alt0 vertical reflection I Horizontal shift h units vertical shift k units I Vertex h k February 13 2015 Section 16 Continued Announcements a MyMathLab hw 8 due on Sunday b No Class Monday c EampN 17 due Wednesday d Chapter 1 Review assignment a Given Wednesday b Due on Friday 220 0 Transformations Continued 0 Standard Form I What ab and c stood for 0 Transformation Form I All the coordinates and how to plug in the numbers into the equation 0 Completing the Square I Take from standard to transformation form 0 Steps to follow I Factor coefficient of xquot2 out of the first two terms if there is one in front of the first term I Add and subtract a quantity 0 Note This will give you a zero 0 Ex If you had a 4 in the b place then you will be adding and subtracting a 2 o XIntercepts o The number of xintercepts will vary depending on where the line is on the graph o If 4acgtbquot2 I There will be 0 intercepts on the graph o If 4acbquot2 I There will be 1 intercept on the graph o If 4acltbquot2 I There will be 2 intercepts on the graph 0 Quadratic Formula I Used to determine the xintercepts of fxaxquot2bxc I Memorize the formula because it will be helpful in finding the xintercepts on the graph and it will help in finding the vertex as well 0 Position Function I T seconds after launch I St16tquot2VnottSnot o Vnot initial velocity 0 Snot initial height above the ground 0 Tgt or equal to O
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