Question

Write an equation to match each graph:

Answer 1

Write an equation to match each graph.

Solution:

The first graph is V shaped graph centered at origin, (0,0) and the graph is not shifted or translated. So, the equation of first graph is,

y=|x|

The second graph is V shaped graph centered at (1,0) and y=|x| is horizontally shifted right by 1 unit. So, the equation of second graph is,

y=|x-1|

The third  graph is also V shaped but, it is inverted V graph centered at (0,1) . As, the graph is inverted V So, the graph must have y=-|x|. But, as the center is (0,1). So, the graph is shifted up by 1 unit. So, the equation of the third graph is,

y=-|x|+1

The fourth graph is shifted V graph, whose center is (1,-1). So, y=|x| is shifted right by 1 unit and down by 1 unit. So, the equation of fourth graph is,

y=|x-1|-1

The center of fifth graph is (-1,0), So, y=|x| graph is shifted left by 1 unit. So, the equation of fifth graph is

y=|x+1|

Answer 2

The equation should be y=|x| BUT i am not 100%. there would be no shifts because the vertex is on the origin.