Find the vertex of absolute value function given below and find the direction of opening.
Problem 1 :
y = 1/4│x + 4│- 9
Problem 2 :
y = -2│x + 1│+ 6
Problem 3 :
y = 4│x - 3│
Problem 4 :
y = -1/2│x│+ 3
Problem 5 :
y = -5│x - 8│- 5
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) 3 5 7 9 11 12 |
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 ?
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) 3 5 7 9 11 12 |
Boats (sold) 90 120 90 60 30 15 |
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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM