How do I find the equation of the absolute value function below?

Question

The points to plot the absolute value function are: (-5,3),(-4,2),(-3,1),(-2,0),(-1,1),(0,2),(1,3),(2,4),(3,5)

Answer 1

Notice that as the x-coordinate increases, the y-coordinate decreases then increases.  This pattern represents an absolute value function.

 

y = a| x - h | + k

 

where:

a is the leading coefficient

(h, k) is the vertex

 

The vertex occurs at (-2, 0)

 

 

y = a| x + 2 |

 

 

Plug in the point (1, 3) to solve for a.

 

3 = a | 1 + 2 |

 

3 = a | 3 |

 

1 = a

 

 

Then you function is

 

y = | x + 2 |