# FIND VERTEX OF ABSOLUTE VALUE FUNCTION WORKSHEET

Find the vertex of absolute value function given below and find the direction of opening.

Problem 1 :

y = 1/4│x + 4│- 9

Solution

Problem 2 :

y = -2│x + 1│+ 6

Solution

Problem 3 :

y = 4│x - 3│

Solution

Problem 4 :

y = -1/2│x│+ 3

Solution

Problem 5 :

y = -5│x - 8│- 5

Solution

Problem 6 :

The number of boats B a boat dealer sells in each month of the year from March to December can be modeled by the function

B = -15|t - 5| + 120

where t is the time in months and t = 1 represents January.

a) Complete the table of values and then graph the function.

 Time (Months)35791112 Boats (sold)

b) What is the maximum number of sales in one month ?

In what month is the maximum reached ?

c) What is the minimum number of sales in one month ? In what month is the minimum reached ?

Solution

1)  Vertex (h, k) = (-4, -9), a = 1/4, it will open up.

2)  Vertex (h, k) = (-1, 6), a = -2, it opens down.

3)  Vertex (h, k) = (3, 0), a = 4, It will open up.

4) Vertex (h, k) = (0, 3), a = -1/2, it will open down.

5)  Vertex (h, k) = (8, -5), a = -5, it will open down.

6)  a)

 Time (Months)35791112 Boats (sold)9012090603015

b)  Maximum sales = 120 boats

At the month of may, the maximum sales has reached.

c) the minimum number of boats sold is 15 and in the month of December.

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