Any absolute value function will be in the form
y = a|x - h| + k
Here (h, k) is vertex.
Vertex can be minimum or maximum point.
Here a represents slope,
Find the vertex of absolute value function given below and find the direction of opening.
Problem 1 :
y = 1/4│x + 4│- 9
Solution :
y = 1/4│x + 4│- 9
Comparing the given function with
y = a │x - h│+ k
y = 1/4 │x - (-4)│- 9
Vertex (h, k) = (-4, -9)
a = 1/4
It is positive, so it will open up.
Problem 2 :
y = -2│x + 1│+ 6
Solution :
y = -2│x + 1│+ 6
y = a │x - h│+ k
y = -2 │x - (-1)│+ 6
Vertex (h, k) = (-1, 6)
a = -2
It is negative, so it opens down.
Problem 3 :
y = 4│x - 3│
Solution :
y = 4│x - 3│
Compare with
y = a │x - h│+ k
y = 4 │x - 3│+ 0
Vertex (h, k) = (3, 0)
a = 4
It is positive, so it will open up.
Problem 4 :
y = -1/2│x│+ 3
Solution :
y = -1/2│x│+ 3
Compare with
y = a │x - h│+ k
y = -1/2 │x - 0│+ 3
Vertex (h, k) = (0, 3)
a = -1/2
It is negative, so it will open down.
Problem 5 :
y = -5│x - 8│- 5
Solution :
y = -5│x - 8│- 5
Vertex (h, k) = (8, -5)
a = -5
It is negative, so it will open down.
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