Write the equation of an absolute value function whose vertex is located at (-1, 3) and passes through (4, 1).

Step-by-step explanation:

The formula for the absolute value function in vertex form is:  

f(x)= a|x – h| + k

where:

(h, k) = vertex

a =  determines whether the graph opens up or down.

h = determines how far left or right the parent function is translated.

k =  determines how far up or down the parent function is translated.

Given the value of the vertex, (-1, 3), substitute its values into the vertex form:

f(x)= a|x – h| + k    

f(x)= a|x + 1| + 3  

Next, use the other given point, (4, 1) to solve for "a":

1= a|4 + 1| + 3

1 = a|5| + 3

1 = 5a + 3

Subtract 3 from both sides:

1 - 3 = 5a + 3 - 3

-2 = 5a

Divide both sdies by 5:

= a      

Therefore, the equation of an absolute value function is:

the opening of this porabola is facing up

step-by-step explanation: