Math 1031 College Algebra and ProbabilityChapter 2 WorksheetOctober 5, 20101. (a) Graph the equations y = |x| and y = |x + 1| by plotting points.Be sure to label both axes and all intercepts.x yx y(b) Do either of the graphs from part (a) have x-axis symmetry,y-axis symmetry, or symmetry about the origin? Explain both interms of your graph and by computing.(c) Graph the equation y = −2|x + 1|. Label both axes and allintercepts.x y(d) Graph the equation y = −2|x + 1| − 3.x y(e) There are two lines that make up the graph in part (d). Find theequation of each of these lines.2. (a) Graph the line 2x + 3y = 6 by finding the x- and y-intercepts. Besure to label both axes and all intercepts.(b) Find an equation for the line which is parallel to 2x + 3y = 6 andwhich passes through the point (−1, 2).(c) Find an equation for the line which is perpendicular to2x + 3y = 6 and which passes through the point (−1, 2).(d) Graph the lines from parts (b) and (c) on the same coordinateplane as the line from part (a). Does your graph make sense? Howcan you tell?3. (a) Determine the constant you would have to add to 2x2+ 4x inorder to make it a perfect square.2y2− 4y +(b) Determine the constant you would have to add to 2y2+ 6y inorder to make it a perfect square.2x2+ 6x +(c) Show that the graph of the equation2x2+ 2y2+ 6x − 4y − 23/2 = 0is a circle by writing the equation in standard form.(d) What is the center and radius of the circle from part (c)?(e) Graph the circle from part (c).(f) Show that the point (−3/2, 4) lies on the circle. How far is it from(−3/2, 4) to the center of the circle? Confirm your answer using thedistance