Expert: Richard J. Raridon - 3/17/2010

Question
HI could you please help me with the this question - The Cross Section of the roof of a house is modelled by the function y= -5
|x-12|+5, where y>0 or y=0 I need to find the slope, height, and lengths including the base. Then I need to state what transformation must be applied to the graph of y=|x| to obtain the graph of y= -5
|x-12|+5, where y>0 or y=0 I found the slope to be 5/12. The peak of the roof is at (12,5)Base=24 units Would the height be 12? and each side be 13 units. I hope i did this part right. Now when it comes to explaining the transformation I'm totally lost. Could you please help. Thanks

Answer
I don't quite understand your equation.  If it's y = -5|x-12|+5, that will work going up and will give you y=5 when x=12 and a slope of 5/12.  However that won't work coming back down.  
From x=12 to x=24 you would have y = 5 -(5/12)|x-12| and the slope would be -5/12.  By the way, the base is 24 and the height is 5.  The slopes are 13.