Precalculus Notes                                         Lesson 1.2 Graphs of Equations 
       Example 1:  Find the x and y-intercepts of                  
       Replace x with zero to find the y-intercept.      
       Replace y with zero to find the x-intercept.     
        
                                        Symmetry 
         TYPE          SAMPLE             GRAPHICAL TEST                 ALGEBRAIC TEST 
                                                                                   
         x-axis                         If (x,y) is on the graph,        Replace y with –y 
                                           then so is (x, -y).                     
                                                                                   
                                                                                   
         y-axis                        If (x, y) is on the graph,         Replace x with –x 
                                           then so is (-x, y).                     
                                                                                   
                                                                                   
         origin                        If (x, y) is on the graph,         Replace x with –x  
                                          then so is (-x, -y).              and y with –y 
                                                                                   
                                                                  In each case, simplify and  check 
                                                                     for an equivalent equation 
        
       Example 2:  Use algebraic tests to check for symmetry.              
             x-axis                        y-axis                         origin 
        
        
        
        
        
       Example 3:  Find the intercepts and test for symmetry.  Then sketch a graph of          . 
        
        
        
        
        
        
       Standard Form of the Equation of a Circle                                         
       The point (x,y) lies on the circle of radius r and center (h,k) if and only if 
                                          (    )   (   )       
        
       Example 4:  What are the center and radius of the circle whose standard form equation is 
                                          (     )           
                                                (   )      
        
              
        
        
       Example 5:  The point (4, 5) lies on a circle whose center is at the origin.  Write the 
       standard form equation of this circle. 
        
        
        
        
        
        
        
        
        
        
        
        
        
        
       Homework:  Pages 21 – 23 complete #9, 23 – 39 odd, 41 – 43, 71-76, 77 – 83 odd