Question

Identify the vertex

y=|x-2|+1

y=-|x+5|+4

My answers
1.(2,1)
2.(5,4)

Answer 1

| 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 )