Find the area of the region that lies below the graph of y = 3 - |x - 1| + 5 but above the x-axis.
+129771 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
