In the same coordinate plane, graph y= a l xl for a = -2,-1/2, 1/2. What effect does A have on the graph of y= alxl? what is the vertex of the graph of y= a lxl?

1 Answer
Oct 14, 2017

Answer:

The coefficient #a# determines the sign of #y# and slope of #y# for both negative and positive values of #x#

The vertex of #y# is #(0,0): forall a in RR: a!=0#

Explanation:

#y = aabsx#

The coefficient #a# determines the sign of #y# and slope of #y# for both negative and positive values of #x#.

Consider the three graphs of #y# below where #a=-2, -1/2, 1/2#

Graph 1 #(a=-2)# #y<0: forall x in RR#
Slope: #+2# for #x in (-oo,0)# and #-2# for #x in (0, oo)#
graph{-2absx [-10, 10, -5, 5]}

Graph 2 #(a=-1/2)# #y<0: forall x in RR#
Slope: #+1/2# for #x in (-oo,0)# and #-1/2# for #x in (0, oo)#
graph{-1/2absx [-10, 10, -5, 5]}

Graph 3 #(a=1/2)# #y>0: forall x in RR#
Slope: #-1/2# for #x in (-oo,0)# and #+1/2# for #x in (0, oo)#
graph{1/2absx [-10, 10, -5, 5]}

The vertex of #y# is #(0,0): forall a in RR: a!=0#