# Which of following is a key property of the absolute-value parent function?

+1 vote
Which of following is a key property of the absolute-value parent function?

A.) It has a slope of 1 on the right half.
B.) It is in quadrants III and IV.
C.) It is U-shaped.
D.) Its vertex is not at the origin.
reshown Oct 3, 2014

Absolute value parent function is y = | x |

The sign is positive so the graph looks like up ward V.

Find the vertex of the graph  y =  | x |

x = 0

For  x = 0 , y = |0|

y = 0

The vertex of the graph is ( 0,0).

To graph the equation, we need some more points to make more accurate graph.

 x y = |x| (x, y ) -3 y = |-3| = 3 (- 3, 3) -2 y = |-2| = 2 (-2, 2) -1 y = |-1| = 1 (-1,1) 1 y = |1| =1 (1, 1) 2 y = |2| = 2 (2, 2) 3 y = |3| = 3 (3,  3)

Graph

1.  Draw a coordinate plane.

2.  Plot the vertex , points and connect these points.

Observe the graph it is in first and second quadrants.

It has a slope of 1 on the right half and has slope of -1 on the left half.

Option A is correct .