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# COLLEGE ALGEBRA MA 109

UK

GPA 3.54

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## Popular in Mathematics (M)

This 21 page Class Notes was uploaded by Kennith Herman on Friday October 23, 2015. The Class Notes belongs to MA 109 at University of Kentucky taught by Lee Roher in Fall. Since its upload, it has received 9 views. For similar materials see /class/228137/ma-109-university-of-kentucky in Mathematics (M) at University of Kentucky.

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Date Created: 10/23/15

g a Shm y Lim ngw Pc u ymrgm a g Chapter 6 Wha 2 3mm a mnaa y kmaw Linear Quadratic Wha 6k gyms a n ady 39n iWQDVU LEW6335quot 1 Lx ax b F what happens if bgt0 blt0 b0 agt0 alt0 1ltalt1 a 0 uadm c is undefined Negative Equation Fovme Slope Intercept y mx b Standard Ax By C Horizontal y b W Vertical X a This brings us back to the concept a linear uation has a degree of 1 ream3n a mym em one shrewd thee allolle ice t identifyquot lab The Equation Form 7 Direction quot Parallel Slope Perpendicular a Sm Wham g new regarding L naav pm yu mm a s 7 Lx 4x 7 if you need to find the zeroes X intercept solve for 0 etc Change the format Lx 4x 74 X would have to equal 74 for Lx O Wilma53 51cm yam a veae y knew L mav uadn a39a a Qxaxbxc what happens if 1ltalt1 a 0 a 0 a is undefined shag Eas gss me 553 537 gmadva a ee 1 Qxax2bxc Factored form Qx ax px q where pltq Now what happens 042 am Mx Ea n a 2 sz 39pq OXq x E 421 Emmi q 517 a gt ID 39 Wap 39XPgt 39Q X0 39pq 39XqquotQx0 Qx gt O pow Qx lt O ne m 7 nmmal n nnn Qx gt 0 p0 Nnm P i o 39 lt 0 116 qua 0 7W oneao m ce Emamm Make some connections with prior knowledge 2amp5 Wharf makes an eogcaanfs cotm caao ra c The degree is 2 0 y X2 y aX2bXC y axh2 k y aXI0X0I Wharf marines aim Maoiin a rc y X2 the basic 7 y aX2bXC Standard Form y axh2 k Vertex Form or y axpX q Intercept Formv Given any one of the equations you should i be able to convert it into another form 39 except for the basic Time EQ E o vertex 00 line of symmetry giansdiemi Freirm y a a etme n c yintercept 397 b2a xcoordinate of the vertex use substitution to find the ycoordina x b2a is the line of symmetry Now you can graph it 1 1028 58 y 8 x 210 23 tted pt fogrm gs to O v epts Intercept Fotrm y E aamngojmanj f p ampq xintercepts 3 a opens updown wideskinny can expand to find the vertex and line of symmetry n t ew a gnaufp mg t an rotm a tcou39 tr am m me at ma aticom EXPLCQRREEE What does a denote What does c denote How do these coefficients effect the graph Heading me made Ex inter cep s 39 the quadratic 1 formula will work 5 every time This should be familiar now match it to the text mewv 39 mgl man pu a mg Tame eqrm Vb 4ac veaila this iim fm Ewe palms ivb2 4ac 2a 39 and rename Bveaak this mm EW pagans x bivb2 4ac 2a 343 may qwazz m qua n beewmes Qx au2 M if M lt 0 No real roots if a gt 0 Minimum if a lt 0 Maximum if M 0 or a double root 77 same idea regarding maxmin if a gt 0 Minimum if a lt 0 Maximum Th m lt aicawum Wha ha a team Ex vemmm Vaniiuess Maximums amid Minimums Find yourvertex 39r b2a How do you know if it will be a maximum or a minimum Identify the intervalsQx 39 negativeQx positive 11112008 Looking closely at a function Chapter 9 Quick Review of Parameterization y3x24x5 Point P62 X6u y2v 2v36u246u5 2V33612UU2244U5 2V10836U3U2244U5 2V10836U3U2244U5 V13540u3u2 X6u y2v y 213540X63x2 12x36 Linear Approximation using Polynomial Parameterization 11112008 y4X2 2 12 What do we do first parameterize the function Now how about a circle x2 y2 25 What is the equation of the tangent line at 34 Now how about a circle Cj o X2y225 Writing the equation of a line O What do you need to know O Then what do you do 11112008 Find the tangent line when X 2 O y2x23x1 Find the tangent line when X 2 Oy2x23x1 ifx2 O y22232 1 Oy8 61 y3 23 Xu72 yv8 O v32u223u 21 O v32u2 8u83u 61 O V5U I 39 O y 35x2 V5X7 O As indicated in the diagram which is not to s ale the tangent line to the grap 0 fx x25x24 at x 12 meets the Xaxis at an angle AOB whose tangent is The angle AOB measures radians 11112008 How can you find angle measures A Use trigonometry O What do you need to use trig O How can you find it given this situation A Looking at the tangent line A O fx x25x24 O atx 12 O What information 2 can you find using this 11112008 Looking at the tangent line A O fx x25x24 O atx 1 O Find the tangent line Looking at the tangent line A O 12 x25x24 O 12 122L 39 1224 O 121447o 24 2 O 12 190 O A12190 11112008 Using parameters A fx x25x24 A12190 x12u y190v 190v12u2512u24 um 4 a O v29uu20 A x 12u y190v Using parameters A v29uu2o y 190 29x12 o y 190 29x3480 12 a y29x 158 x12u y190v Using parameters A v29uu2o y 190 29x12 o y 190 29x3480 12 a y29x 158 7158 x12u y190v Looking at the tangent line Diagram is not to scale 12190 E Now what do you know 11112008 Looking at the tangent line Diagram is not to scale Looking at the tangent line Diagram is not to scale Now you have 2 sides you can find the desired angle Looking at the tangent line i gram is not to cale tan 9 34812 must find degree to ange to radians tan 9 tanquot34812 11112008 Another way to find the tangent line O Derivative O What is the Derivative

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