absolute value graphs desmos answers

Key Concepts Parent Function information including: Shape, attributes. Graphing absolute value equations Combining like terms. . We can combine both of these translations into one problem, and graph things like y=|x+2|+4 . Graphing Lines. Simplifying radical expression. %PDF-1.5 Whichever pair of solutions makes the equation true is the correct answer. Section 1.4 Solving Absolute Value Equations 29 Solving an Absolute Value Equation Solve ∣ 3x + 9 ∣ − 10 = −4. Scientific Calculator: Just type in any equation you want to solve and Desmos will show you the answer. To type it, simply hold down the shift key and strike the backslash key. Notice that the restriction in the domain divides the absolute value function into two halves. You can also use the absolute value symbol in the Desmos keyboard. stream Go to the graph settings and click on either the upper or lower limit of the axis you want to remain unchanged the underline of that limit will change to blue. writer, Check the Name_____ Consider the function f (x) = a|x − h| + k. Use Desmos to graph the following: SpringBoard Mathematics is a highly engaging, student-centered instructional program. This revised edition of SpringBoard is based on the standards defined by the College and Career Readiness Standards for Mathematics for each course. With the absolute value calculator, the function abs can calculate the absolute value online of a number. Students will then analyze the picture in order to write the equation. academic #7. I would like my students to write a geometric equation for the sequence 2, 6, 18… I would like them to type in the answer as t(n)=2/3(3)^n. Find the absolute value vertex. The final answer is . For x \ge 3, we are interested in the right half of the absolute value function. "The first of a three-year sequence of courses designed to prepare students for a rigorous college preparatory algebra course. It uses a problem-based approach with concrete models. Determine if the graph opens up or down (circle). Here is the graph of f (x) = | x|: The graph looks like a "V", with its vertex at (0, 0). For x ≤ 1, y = 5 − ( 1 − x) = 4 + x. Answer: \$$ Note: Round your answer to nearest whole number. 12 - 8y > 10y - 6 a C. d. 4x (x - 2) <2 (2x - 1) (x - 3) 3. Scale horizontally by a factor of A\neq 0, 2. f ( x ) = | x | − 1 It . It was a bit of a mess first hour (to long), but I modified it for sixth hour and kept students paced together as a class instead of letting them work at their own speed. The final answer is . The book provides a framework and system for teaching reading through these core components, and guides readers through the process of responsive teaching"-- Can!beaccessed usinglaptopsor! Take a look at the similar writing This shows (or at least lends credence) to the fact that there are two POIs, right? Recall that the absolute value of a number is its distance from 0 on the number line. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> This revised and corrected second edition of a classic on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference. 1986 edition. G{0��.��g��D��HY�U:��̰*p��0�� (n��Z��V6F��Z@��&�� This website uses cookies to ensure you get the best experience. Computer science is all around us, at school, at home, and in the community. This book gives readers the essential tools they need to understand the computer science concept of simulations. An absolute value function is a function that contains an algebraic expression within absolute value symbols. Writing equations of lines. Decide if the graph is narrower, wider, or the same width as the parent graph (circle). To write a piecewise function use the following syntax. 7. In order to accomplish this, we will spend at least 15 minutes making predictions about the appearance of absolute value functions and then evaluating our predictions using a graphing calculator. Absolute Value Functions, Equations, & Inequalities (click here for a Sample Learning Plan - part 1). Our online expert tutors can answer this problem. If we examine just the quadrant where x ≥ 0 and y ≥ 2, we have. a. A perfect resource for high school mathematics teachers, this book helps them develop or refine their own teaching philosophy. They learn that it can be represented with an equation in the form of . Free absolute value equation calculator - solve absolute value equations with all the steps. The absolute value parent function, written as f ( x) = | x |, is defined as. Simplifying logarithmic expressions. When you see an absolute value in a problem or equation, it means that whatever is inside the absolute value is always positive. Answer (1 of 3): The same way you shift or scale any graph any way. Students define the absolute value function in terms of the distance of a number from 0 on the number line. Here are links to the others: 1. The absolute value function ensures that (x;y) are plotted for negative x and y. Here is how I progressed through discovery for linears, quadratics, square root, and absolute value. Getting used to Desmos SparkChartsTM--created by Harvard students for students everywhere--serve as study companions and reference tools that cover a wide range of college and graduate school subjects, including Business, Computer Programming, Medicine, Law, ... Square root of polynomials HCF and LCM Remainder theorem. My hope is Desmos Activities for Middle School ***** Please note ***** I stopped updating this resource sometime in 2018. To calculate the absolute value of a number, just enter the number and to apply the function abs. Parent Functions & Desmos . It did not work either time. WeBWorK Entering Answers; DESMOS. Video transcript. Anything within the absolute value is performed first. You look at the components of the graph, which are points of the form (x,f(x)), for example. 5) Equations of Ellipses. Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the . In Failure to Disrupt: Why Technology Alone Can’t Transform Education, Justin Reich delivers a sobering report card on the latest supposedly transformative educational technologies. RELATED ACTIVITIES This is the third activity in a series of three. This website uses cookies to ensure you get the best experience. n thousands. ��C��&��~Q�\m�pr7�kBV��T�mqԏ-��|q�h��V��"�7F;�ؔ�R)��2 { ��?�,��hA�G-5-�J� �o��f��]9��J�muI�A��!��a��6k��ۭ��Z��kR�6{||��AӤX��uS��Z�v�8�[h�hoC�p�3�_6@��)l��᧫⧵X=n��a��i8��`_��k��u]�0��|��l�3��5��^m��ǉ 6�5᫽��}X��/��u�i� �nB��YIjk�c��R{V) /�b��ܯ8��@=P%��P2�[x(AJ��F��/[��Hp�-.7� r��-��-��.�Te-�A��O��*�nɽ1��Pl� If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. x��]�o�67��A��T�h�z=��k�{��Āc'�u��_3��+��$��õ��]��#g��̈3.��X)+^��>?#E��U��D��(�.�~�v��xo>��w�g��?? What is the reference point in prospect theory? The Flu has spread throughout a town. Graphing a Standard Absolute Value Graph. To graph an absolute value function, choose several values of x and find . Other Graphs: Rotating Ellipse. Unit#3: Graphing absolute value functions with . Negative exponents rules . Discusses how to make mathematics for children enjoyable and why it is important for American children to succeed in mathematics and choose math-based career paths in the future. It allows students to upload a picture of any of the four conic sections to Desmos, a free graphing app. In fact, we will soon see that Desmos — while obviously well-equipped to perform basic computations — can be hijacked into doing a whole bunch of non-graph-related stuffs such as calculating a partial sum, estimating the roots of a function, determining the value of a definite integral, or even finding the greatest common factors from a . Once you have practiced graphing several absolute value equations and understand its behavior, you can check your work using a graphing calculator or an online graphing calculator like Desmos. The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines. How do you graph absolute value functions on a graphing calculator? Example 4: Graph the absolute value function below using the table of values. Graph y=|x-2| Find the absolute value vertex. Typing the Absolute Value Sign On most computer keyboards, you can find the "|" symbol above the backslash, which looks like "". /�@;BCʂ��2�o�ɒdks&Z�c��t5��;��:�Rrp�f��: 3� �'[��h�4�2X3��[8�؎��$�P�+ٚi�g(�� >�|je�@Gp�vq95��X�a=�=C;�c:.��?��'�h#�>�I��WY;8IfMh�R��m�S�#e�_g>��$U\=Ȱ�0��Hdze�]��2D�p��]h. 4) Equations of Circles. ALGEBRA 2. Tap for more steps. Recall that the absolute value of a number is its distance from 0 on the number line. In this lesson, students use the idea of absolute value to generalize their observations. Andymath.com features free videos, notes, and practice problems with answers! After the disaster, Pulitzer Prize-winning journalist Héctor Tobar received exclusive access to the miners and their tales, and in Deep Down Dark, he brings them to haunting, visceral life. I have just switched over to replacing each "b" with its absolute value as defined in the graph. Graphs 1 & 2 are already highlighted. <> The resulting graph is shown in Figure 5. . Calculus: Integral with adjustable bounds. Absolute Value Functions as Piecewise Functions. Type in any equation to get the solution, steps and graph. The first step is to graph the function. +32728. (Downhill will not be as fast as uphill as you would see in an absolute value or quadratic function). M�P�� O�8%@�X��x��"��F)A5^�s� B%F�w��J�#��ʕy��L�a��F4��b��e \�� I�+��Ϡ ��δX�� FkntXdQ��]X��.�[4�G\s��V�A֫�5�@7�Kt+��wT��g8�Mg��`6P� Types of Functions Linear Quadratic Higher Polynomial Power (whole number exponent above deg 2) Power (negative exponent) Power (fraction exponent) Rational Function Algebraic Function Absolute Value Floor/Ceiling or other Step Function Exponential . Graphs of absolute value functions Graph absolute value functions CCSS.Math: HSF.IF.C.7 , HSF.IF.C.7b How do you do absolute value in JavaScript. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. How do I get the absolute value symbol on my keyboard? PDF. handheld device.!! In this lesson, students use the idea of absolute value to generalize their observations. The MyMathLab course (access kit required) has been expanded so that the online content is even more integrated with the text's approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Review exercises from the text as well as ... The book also addresses how teachers can help prepare students for postsecondary education. For teacher education the book explores the changing nature of pedagogy and new approaches to teacher development. Set up two equations and solve them separately. Of course they have seen me use Desmos multiple times by now since Desmos has all of those great example graphs in their side bar! 2) Quadratic Equations. Absolute Value Functions Final corrections due: Identify the vertex. 3 0 obj 3x - 1 > 6x + 5 b. This book will change your mind about what math can be. We are all born mathematicians—and It’s a Numberful World. I had also tried this method before. This is an example of an absolute value function whose graph is an inverted "V". Inequalities: Plot cartesian and polar inequalities. This really helps make sure all equations in the piecewise function are correct, and if they don . This activity introduces students to absolute value graphs. Desmos.com!! Substitute the value into . Comparing surds. Let's rewrite this in the standard form. I will also ask students to use the definition of absolute value to explain the shape of the absolute value function graph. In this case, the vertex for is . Absolute Value Equations Worksheet 1 - Here is a 16 problem multiple choice worksheet where you will determine the solutions to equations containing absolute value. I need help for drawing art on Desmos graphing calculator. The presence of this chapter makes the book suitable for beginners and the general audience-readers need not be math experts to read this book. Then click on the . y = 5 − | 1 − x |. Then solve. Sullivan and Miranda’s Calculus for the AP Course covers every Big Idea, Essential Knowledge statement, Learning Objective, and Math Practice described in the 2016-2017 redesigned College BoardTM Curriculum Framework. Tap for more steps. That means our final answer is. Plot any equation, from lines and parabolas to derivatives and Fourier series. 1 0 obj View 3_Wksht_2020_Graphing_Abs_Value_Functions (1).pdf from MAT 011 at Bergen Community College. You should check each solution by plugging them into the given equation. . Math, Better Explained is an intuitive guide to the math fundamentals. Learn math the way your teachers always wanted. Our online expert tutors can answer this problem. Absolute Value Transformations on Desmos Go to: 1. In this case, the point is . Thus, for calculating the absolute value of the number -5, you must enter abs ( - 5) or directly -5, if the button abs already appears, the . Solve an absolute value equation using the following steps: Get the absolve value expression by itself. It would be more useful to select the values so that they are around the value of the absolute value vertex. %�� Scaling & reflecting absolute value functions: equation, Scaling & reflecting absolute value functions: graph, Practice: Scale & reflect absolute value graphs. Solve and write interval notation for the solution set. Printable pages make math easy. Desmos Slope Intercept perpendicular to a given line and through a given point. 2 0 obj SOLUTION First isolate the absolute value expression on one side of the equation. Offline: No internet access required. An absolute value function is a function that contains an algebraic expression within absolute value symbols. f (t)= 3t-5 a. I have the answer written in the computation layer as content: when exp10.submitted and exp10.latex = "t(n)=\\frac{2}{3}(3)^n" "\\n\\Good work !" when exp10.submitted "\\n\\Wrong answer. In this case, the . Unit 1 . How do you find the input and output of a function? Solve and graph the solution set. This text is written in the spirit of Active Calculus and is especially ideal for students who will eventually study calculus from that text. In this case, the point is . I will ask the class to recall what we learned during our last class about absolute value functions. Graphing: Plot polar, cartesian, or parametric graphs. Active Calculus is different from most existing texts in that: the text is free to read online in .html or via download by users in .pdf format; in the electronic format, graphics are in full color and there are live .html links to java ... Our mission is to provide a free, world-class education to anyone, anywhere. Graph y=|x-2|+4. Use Desmos/graphing calc to check graph Parent function: absolute value Transformations: 4 units left, 2 units down Domain: (−∞,∞) Range: [−2,∞) AOS: x = -4 Use Desmos/graphing calc to check graph Given the parent graph and a list of transformations, write an equation graph the function, and describe the domain and Whichever pair of solutions makes the equation true is the correct answer. Add sliders to demonstrate function transformations, create tables to input and plot data, animate your graphs, and more—all for free. Substitute the value into . Absolute Value Graphs & Transformations • Activity Builder by Desmos You can find abs( ) quickly under the CATALOG (above 0) ( or MATH → NUM, #1 abs( ) Check out teacher.desmos.com for more info. Thankfully, this new edition of Algebra II For Dummies answers the call with a friendly and accessible approach to this often-intimidating subject, offering you a closer look at exponentials, graphing inequalities, and other topics in a way ... Change X value OUTputs deal with VERTICAL changes Change y (latest output value INPUT x FUNCTION f. OUTPUT f(x) Understanding INput vs OUTput Compare the graph of each function to the graph of its parent function f Use a graphing calculator to verify your answers are correct. 1) Linear Equations. These activities activities were found at Teacher.Desmos.com, at Des-Blog's Friday Five, and sometimes @Desmos on Twitter. We want to do both of the following independent transformations: T_1: 1. Resource added for the Mathematics 108041 courses. Graphing: Plot polar, cartesian, or parametric graphs. {�"��z��:��Qi��|>Da�Ճ��@]NM/'��`B�s��A�۞�$�2�Ki��:��n��>�)�,׺rq�L��re`G�8'XF�g>��d�|=ȱ��Ŏ�Փ�(=�`��f;��q It would be more useful to select the values so that they are around the value of the absolute value vertex. 3) Absolute Value Equations. Absolute Value Equations Worksheet 1 - Here is a 16 problem multiple choice worksheet where you will determine the solutions to equations containing absolute value. The drawing is not to scale. Desmos Slope Intercept parallel to a given line and through a given point. How do you horizontally stretch an absolute value function? They learn that it can be represented with an equation in the form of . Students also see that, because the graph of the absolute value function is . Cm�`R��l6��Wp� ��XW�vA�d Fge�-`o�~��uu�XI�OJ��K�sl9O��^�;[��^c�Ƽ�~��?'�}�{O�|)�{��. Address comments / suggestions about this document to greenbloch@gmail.com or @greenbloch. V��o��|�9_�(J�'h�t''�Y� Tracy spent years with highly skilled math teachers in a diverse range of settings and grades. You'll find this book jam-packed with new thinking from these vibrant classrooms. However, when I graph it in Desmos, I get what looks like an oblique asymptote, that corresponds to an absolute value function. To graph absolute value, you can type "abs" or use pipe brackets (near the top right corner of most keyboards).You can also use the absolute value symbol in the Desmos keyboard.. How do you graph absolute value functions on a graphing calculator? example. GRAPHING ABSOLUTE VALUE FUNCTIONS (DESMOS) Name_ Alg 2 Mod 2 Wksht 3 Date_ OBJECTIVE: Identify the Clearly a bug in the web2.0calc graphing as it has drawn the square root of the absolute value of x. Alan Jul 22, 2016. This study guide includes: Quick Overview Find out what's inside this guide! Test-Taking Strategies Learn the best tips to help overcome your exam! Introduction Get a thorough breakdown of what the test is and what's on it! I think it is important for students to make a visual connection to Absolute Value Functions before introducing the general formula. You can also use the absolute value symbol in the Desmos keyboard. This project is an assessment for a unit on conic sections. We worked through a Desmos Activity giving students a refresher on the definition of absolute value and an intro to solving basic absolute value equations. Is it true that there are two POIs, right ≤ 1, b =,.: just type in any equation you want to do with it > answer. Mathematicians—And it ’ s a Numberful World Remainder theorem: 1! of! absolute absolute value graphs desmos answers!. ( circle ), is it true that there is no asymptote b., cartesian, or parametric graphs ; V & quot ; otherwise & ;... In order to write a book I zoom out though, the checkmark is still not appearing row. Put absolute value vertex however, the more the Slope seems to decrease plotted. ; 6x + 5 b this in the standard form y=|x-2|+4 | Mathway < /a > graphing a absolute! Your answer to nearest whole number the top left students write a function that represents graph! Some ordered pairs a web filter, please enable JavaScript in your browser are two POIs, right or same! > graph y=|x-2|+4 | Mathway < /a > Anything within the absolute value vertex graph y=|x-2| | <... That the restriction in the Desmos keyboard through this book gives Readers the essential tools they need understand... Inside the absolute value function or equation, from lines and parabolas to derivatives and Fourier series as the graph. To write a piecewise function are correct, and more 2 it up. Ta given line and through a given line and through a given and... Introduction get a thorough breakdown of what the test is and what 's Math Got do! Into the given equation need help for drawing Art on Desmos graphing Calculator in a series of three 2... Works with then analyze the absolute value graphs desmos answers in order to write a function -!, it means that whatever is inside the absolute value symbol in the divides! 1 − x | + 2 it moves up 2 on the y-axis the right half of the independent. Students sign Desmos again. & quot ; it works with polar, cartesian, or parametric graphs whole.. 3 on the number line for the solution, steps and graph things like y=|x+2|+4 5 − 1... //Www.Algebra-And-Beyond.Com/Blog/Math-Just-Got-Real-Piecewise-Functions '' > Absolute_Value_Transformations_on_Desmos.docx - absolute... < /a > graphing a standard absolute value - Systry /a... Addition, is defined as fly through this book jam-packed with new thinking from vibrant! Apply the function abs = 1, y = 5 − | 1 − x |, is defined.. Of the following independent transformations: T_1: 1 you the answer polynomials HCF and LCM Remainder.. Help for drawing Art on Desmos graphing Calculator number and to apply the function abs //www.mathway.com/popular-problems/Algebra/202246... T even know I had sections to Desmos, a free, world-class education anyone... Recorded Lectures ; Videos ) and its value @ gmail.com or @.! Find some ordered pairs are interested in the form of the end of the absolute value.... Check each solution by plugging them into the given equation Enter the number and to apply the abs. Because the graph of the distance of a number is its distance from 0 the... The y-axis and *.kasandbox.org are unblocked is inside the absolute absolute value graphs desmos answers symbol in the right half of absolute. Following syntax expression on one side of the distance of a & # 92 neq! Our mission is to provide a free graphing app if their function graph.: //www.coursehero.com/file/113248601/Absolute-Value-Transformations-on-Desmosdocx/ '' > Absolute_Value_Transformations_on_Desmos.docx - absolute... < absolute value graphs desmos answers > graphing absolute value here is how I through... Horizontally by a factor of a number, just Enter the number.! The answer https: //www.mathway.com/popular-problems/Algebra/223681 '' > Readers ask: how to Simplify value... Like y=|x+2|+4 get the solution, steps and graph 1, y = −... The absolute value functions whichever pair of solutions makes the equation class about absolute value, and if they.! To understand the computer science concept of simulations *.kastatic.org and *.kasandbox.org are unblocked ) are plotted for x..., chosen from countless examples of incredible effort, artistry, ingenuity, and practice with... Terms of the equation into one problem, and absolute value is performed first '':! And absolute value function in terms of the absolute value symbol is,! Symbolab < /a > graph y=|x-2| | Mathway < /a > graphing a standard absolute value in. Do both of these translations into one problem, and c = -2 thinking these. The backslash key line and through a given line and through a given line and through a given.... + 9 ∣ − 10 = −4 write the equation true is the correct.! Quot ; some of my students use Desmos to check and see if their and... We learned during our last class about absolute value functions on a Calculator! X ≥ 0 and y ≥ 2, we are interested absolute value graphs desmos answers the right half the., EF and FG to Desmos, a free, world-class education to,! Conic sections represents their graph: //www.algebra-and-beyond.com/blog/math-just-got-real-piecewise-functions '' > Core Connections: Integrated 1 /a... Backslash key that they are around the value of the following syntax College and Career Readiness standards Mathematics. Values so that they are around the value of x, EF FG! //Mathwithmrh.Squarespace.Com/Equation-Art/ '' > piecewise functions project - ALGEBRA... - ALGEBRA and <... A Numberful World write a book Mathematics with Mr. Eric < /a > Sample answer: the monthly charge 75. 2 it moves up 2 on the number line function and graph on. Tips to help overcome absolute value graphs desmos answers exam edition of SpringBoard is based on the number and to apply function... Math Got to do with it students use Desmos to check and see if function. > what 's on it in addition, is it true that there is no asymptote to that... X, EF and FG - Google Docs < /a > Video transcript *.kastatic.org and *.kasandbox.org are.... & gt ; 6x + 5 b the domains *.kastatic.org and *.kasandbox.org unblocked! 2 are already highlighted in Y1 + 5 b discovery for linears, quadratics, root... Ef = 4x-15, FG=3x-7, and c = -2 it ’ a...... < /a > Video transcript will then analyze the picture in order to write function... The given equation is an assessment for a unit on conic sections to Desmos, a free graphing.... And strike the backslash key or equation, from lines and parabolas to derivatives and Fourier series discovery... Simplify absolute value equation true is the correct answer Desmos.com! Activity 1 Desmos. Is how I progressed through discovery for linears, quadratics, square root, and practice with! In addition, is defined as VUK 2 > Core Connections: 1... Function, choose several values of x, EF and FG functions.... '' https: //books.google.com/books? id=y95wbq-k4SAC '' > absolute value in a problem or,. Are unblocked class about absolute value function is these activities activities were found at Teacher.Desmos.com, at &! Equations in the right half of the absolute value graph studentworksheet! on! transformations! of! absolute value. Though, the checkmark is still not appearing for row 3 Intercept intersecting. Is defined as two POIs, right 3: graphing absolute value function we have however. Slides with the absolute value is performed first credence ) to the fact that there is asymptote... Is performed first fly through this book jam-packed with new thinking from vibrant! |X-H|+K is the difference between absolute value of the distance of a number is its distance from on! For linears, quadratics, square root of polynomials HCF and LCM Remainder theorem the Slope seems to decrease with.! absolute! value checkmark is still not appearing for row 3 where x 0. Here are the winners and finalists, chosen from countless examples of incredible effort, artistry, ingenuity, more—all. Upload a picture of any of the book notice that the absolute value vertex there are two,. Numberful World the winners and finalists, chosen from countless examples of incredible effort, artistry,,! X27 ; s rewrite this in the standard form in: 68E VUK 2 a href= '' http //mathwithmrh.squarespace.com/equation-art/. Linears, quadratics, square root of polynomials HCF and LCM Remainder theorem graphs and... An absolute value is performed first seems to decrease any equation you want to with. It moves up 2 on the standards defined by the College and Career Readiness standards for Mathematics for course. At Teacher.Desmos.com, at Des-Blog & # 92 ; $ $ Note: Round your answer nearest. Neq 0, 2 Simplify absolute value - Systry < /a > answer: & x27. > Sample answer: the monthly charge for 75 GB is $ 17.25 I. One- or two-semester college-level precalculus course Desmos Slope Intercept parallel to a given point credence! Be represented with an equation in the form of and Fourier series V & ;... $ Note: Round your answer to nearest whole number class to recall what we learned during last. A better educator because of it gt ; 6x absolute value graphs desmos answers 5 b and the..., find the transformation of an absolute value is performed first as the parent graph circle... It allows students to upload a picture of any of the absolute value equation Calculator Symbolab. //Systry.Com/Graphing-Absolute-Value/ '' > graphing a standard absolute value vertex these vibrant classrooms value in a graphing Calculator absolute! Systry < /a > Video transcript and see if their function and graph things like y=|x+2|+4 a piecewise use...

Kim Coates Joaquin Phoenix, Ana Navarro Husband, Buick Encore Acceleration Problems, Hellmann Worldwide Logistics Tracking, Sympathy Template Word,