+0  
 
0
28
1
avatar

Find the area of the region that lies below the graph of y = 3 - |x - 1| + 5 but above the x-axis.

 Jul 23, 2022
 #1
avatar+124524 
+1

 Rearrange as    ...     y =  8 - abs ( x  -1)

 

This will form a triangle  

 

The max height occurs when x = 1   and the  height  =   8

 

To find the x intercepts we have

 

8 - abs (x -1)  = 0

 

8 =  abs ( x -1)........this sets up  two equations

 

8 =  x - 1             - 8  =  x  -1

x = 9                     x =  -7

 

So the x intercepts are   -7  and 9   and the base of the  triangle =   9 -  (- 7 )  = 16

 

So.....the area =   (1/2) (16)(8)  = 64

 

 

cool cool cool

 Jul 23, 2022

14 Online Users