Question

HELP PLEASE!!!!!!!!!!!

Answer 1

Part 1)
`y=-x^(2)` ---> Translated up by 1 units

Part 2)
`y=x^(2)+1` ---> Reflected across the x-axis

Part 3)
`y=-(x+1)^(2)-1` ---> Translated left by 1 unit

Part 4)
`y=-(x-1)^(2)-1` ----> Translated right by 1 unit

Part 5)
`y=-x^(2)-1` ----> Reflected across the y-axis

Part 6)
`y=-x^(2)-2` ----> Translated down by 1 unit

Explanation:

we know that

The parent function is

`y=-x^(2)-1` ----> this is a vertical parabola open downward with vertex at (0,-1)

Calculate each case

Part 1) Translated up by 1 unit

The rule of the translation is

(x,y) -----> (x,y+1)

so

(0,-1) ----> (0,-1+1)

(0,1) ----> (0,0) ----> the new vertex

The new function is equal to

`y=-x^(2)`

Part 2) Reflected across the x-axis

The rule of the reflection is

(x,y) -----> (x,-y)

so

(0,-1) ----> (0,1) ----> the new vertex

The new function is equal to

`y=x^(2)+1`

Part 3) Translated left by 1 unit

The rule of the translation is

(x,y) -----> (x-1,y)

so

(0,-1) ----> (0-1,-1)

(0,1) ----> (-1,-1) ----> the new vertex

The new function is equal to

`y=-(x+1)^(2)-1`

Part 4) Translated right by 1 unit

The rule of the translation is

(x,y) -----> (x+1,y)

so

(0,-1) ----> (0+1,-1)

(0,1) ----> (1,-1) ----> the new vertex

The new function is equal to

`y=-(x-1)^(2)-1`

Part 5) Reflected across the y-axis

The rule of the reflection is

(x,y) -----> (-x,y)

so

(0,-1) ----> (0,-1) ----> the new vertex

The new function is equal to

`y=-x^(2)-1`

Part 6) Translated down by 1 unit

The rule of the translation is

(x,y) -----> (x,y-1)

so

(0,-1) ----> (0,-1-1)

(0,1) ----> (0,-2) ----> the new vertex

The new function is equal to

`y=-x^(2)-2`