Question

Write the algebraic expression that matches each graph: please help???

Answer 1

All answers in photos

Answer 2

see the attached figures

Explanation:

Part 1) we have

The vertex is the point
`(1,0)`

The equation of the line of the left side is
`y=-x+1`

The equation of the line of the right side is
`y=x-1`

The range of the function is equal to
`y\geq 0`

therefore

The absolute function will be equal to

`y=\left|x-1\right|`

see the attached figure N 1

Part 2) we have

The vertex is the point
`(0,1)`

The equation of the line of the left side is
`y=x+1`

The equation of the line of the right side is
`y=-x+1`

The range of the function is equal to
`y\leq 1`

therefore

The absolute function will be equal to

`y=-\left|x\right|+1`

see the attached figure N 2

Part 3) we have

The vertex is the point
`(1,-1)`

The equation of the line of the left side is
`y=-x`

The equation of the line of the right side is
`y=x-2`

The range of the function is equal to
`y\geq -1`

therefore

The absolute function will be equal to

`y=\left|x-1\right|-1`

see the attached figure N 3

Part 4) we have

The vertex is the point
`(-1,0)`

The equation of the line of the left side is
`y=-x-1`

The equation of the line of the right side is
`y=x+1`

The range of the function is equal to
`y\geq 0`

therefore

The absolute function will be equal to

`y=\left|x+1\right|`

see the attached figure N 4

Part 5) we have

The vertex is the point
`(-1,1)`

The equation of the line of the left side is
`y=x+2`

The equation of the line of the right side is
`y=-x`

The range of the function is equal to
`y\leq 1`

therefore

The absolute function will be equal to

`y=-\left|x+1\right|+1`

see the attached figure N 5