Identify the vertex
y=|x-2|+1
y=-|x+5|+4
My answers
1.(2,1)
2.(5,4)
| x - 2 | + 1 = x - 2 + 1 = x - 1
OR
| x - 2 | + 1 = - ( x - 2 ) + 1 = - x + 2 + 1 = - x + 3
For vertex you must find point where: x - 1 = - x + 3
x - 1 = - x + 3 Add x to both sides
x - 1 + x = - x + 3 + x
2 x - 1 = 3 Add 1 to both sides
2 x - 1 + 1 = 3 + 1
2 x = 4 Divide both sides by 2
x = 4 / 2
x = 2
y = x - 1 = 2 - 1 = 1
OR
y = - x + 3 = - 2 + 3 = 1
Vertex ( 2 , 1 )
- | x + 5 | + 4 = - ( x + 5 ) + 4 = - x - 5 + 4 = - x - 1
OR
- ( - x - 5 ) + 4 = x + 5 + 4 = x + 9
For vertex you must find point where: - x - 1 = x + 9
- x - 1 = x + 9 Add x to both sides
- x - 1 + x = x + 9 + x
- 1 = 2 x + 9 Subtract 9 to both sides
- 1 - 9 = 2 x + 9 - 9
- 10 = 2 x Divide both sides by 2
- 10 / 2 = x
- 5 = x
x = - 5
y = - x - 1 = - ( - 5 ) - 1 = 5 - 1 = 4
OR
y = x + 9 = - 5 + 9 = 4
Vertex ( - 5 , 4 )