College Algebra. Cartesian Coordinates and Graphs. Dr. Nguyen August 22, Department of Mathematics UK

Transcription

1 College Algebra Cartesian Coordinates and Graphs Dr. Nguyen Department of Mathematics UK August 22, 2018

2 Agenda Welcome x and y-coordinates in the Cartesian plane Graphs and solutions of equations Drawing a graph x and y intercepts

3 Contact Info Instructor: Dr. Nguyen Oce: Patterson Oce Tower 705 Oce hours: MWF 10:30-11:45 Canvas website: Online homework, textbook link, syllabus, announcements, exam grades Homework is all done online. See the syllabus for more info.

4 Class Lectures I will present information using my own slides and examples. We will use iclicker REEF polling in class. An announcement on Canvas was sent out with instructions on setting up an account. Set up your account before class on August 31st.

5 Homework Homework assignments are given online. Access the homework site through Canvas Google Chrome is recommended You have homework due every Tuesday and Friday (at 11:59pm), except for the rst one, which is due next Thursday, August 30th. Homework problems range from those which are similar to in-class examples, to those which require you to use or combine concepts and techniques from class.

6 Grades Assessment % of nal grade Exam 1 20% Exam 2 20% Exam 3 20% Final Exam 20% Homework 6% REEF 6% Written Projects 8%

7 Exam Dates All exams are in White Hall room 110 (not the usual room). Any conicts? Contact me so we can arrange an alternate exam session. Exam Date (all Wednesdays) Time Exam 1 September 19 7:30pm 9:30pm Exam 2 October 17 7:30pm 9:30pm Exam 3 November 14 7:30pm 9:30pm Final Exam December 12 8:30pm - 10:30pm Check the syllabus for other important dates.

8 Help and Assistance I hold oce hours. Check the class syllabus for times and locations. You can also me at nicholas.nguyen@uky.edu

9 College Algebra Goal: prepare you to use the basic tools of algebra to solve problems with known and unknown quantities. Know which tool/technique to use Know how to use that tool/technique Know if you used that tool/technique successfully

10 College Algebra MA 109 will demand a lot of your time and eort. You need to participate in class and do the homework in order to do well You need to practice - do not just read the book and slides and assume you get it You can get help: the instructor, tutors, classmates

11 College Algebra What will you get if you succeed in MA 109? It is a prerequisite to MA 123 (Elementary Calculus) Many STEM programs (majors or colleges) require MA 109

12 The Cartesian Plane

13 The Cartesian Plane

14 The Cartesian Plane Quadrants The x and y-axes divide the plane into four quadrants.

15 The Cartesian Plane The x and y-axes are numbered to locate points in the plane.

16 Points in the Plane Each point is located using two numbers: Its x-coordinate: how far to move right or left Its y-coordinate: how far to move up or down

17 Points in the Plane Each point is located using two numbers: Its x-coordinate: how far to move right or left Its y-coordinate: how far to move up or down Together, these numbers are written as an ordered pair: (x-coordinate, y-coordinate)

18 Ex1: Plotting Points Plot the point (1,2):

19 Ex1: Plotting Points Plot the point (1,2): Go right 1 unit, then go up 2 units.

20 Ex2: Plotting Points Plot the point ( 2,0):

21 Ex2: Plotting Points Plot the point ( 2,0): Go left 2 units, but stay on x-axis.

22 Ex3: Plotting Points Plot the point (0, 3):

23 Ex3: Plotting Points Plot the point (0, 3): Stay on y-axis, and go down 3 units.

24 Graphs of Equations with Two Variables The graph of an equation in the variables x and y is the set of all points (a,b) so that x = a and y = b is a solution to the equation. This means if we plug x = a and y = b into the equation, both sides are equal.

25 Graphs of Equations with Two Variables The graph of an equation in the variables x and y is the set of all points (a,b) so that x = a and y = b is a solution to the equation. This means if we plug x = a and y = b into the equation, both sides are equal.

26 Ex4: Point on Graph of y = 1 2 x + 2 Is the point (2,1) on the graph of y = 1 2 x + 2?

27 Graph of y = 1 2 x + 2 Here is the graph of y = 1 2 x + 2. The point (2,1) is on the graph.

28 Ex4: Point on Graph of y = 1 2 x + 2 Let's plug x = 2 and y = 1 into the equation: 1? = 1 2 (2) + 2 1? = = 1 x = 2 and y = 1 is a solution, and the graph displayed this by having the point (2,1) in it.

29 Ex5: Point on Graph of y = 1 2 x + 2 Is the point (3,2) on the graph of y = 1 2 x + 2?

30 (3,2) is not on the graph

31 Ex5: (3,2) is not on the graph If we plug x = 3 and y = 2 into y = 1 2 x + 2, this happens: 2 2 2? = 1 2 (3) + 3? = ? = χ Graphically, this means the point (3,2) is not on the graph of y = 1 2 x + 2.

32 C1: Point on Graph? Is the point (5,6) on the graph of 3y = x 2 7? If yes: type yes and type the number you get on both sides of the equation. if no: type no and type the numbers you get on the left and right sides of the equation.

33 C1: Point on Graph? Is the point (5,6) on the graph of Plug in x = 5 and y = 6: 3(6) 3y = x 2 7? 18? = (5) 2 7? = = 18 Since we got the same number on both sides, the point (5,6) is on the graph of 3y = x 2 7.

34 Next Time Please read Sections 2.1 and 2.2 of your textbook. We will look at the distance formula and midpoints.