Question

PLEASE HELP!!!

1. Describe the Transformations
y=(x−1)2

2. Describe the Transformations
y=12(x+4)2−8
Blank #1 -
Blank #2 -
Blank #3 -

3. Match the transformation of the parents functions with the equation of the new function.
y=2(x+4)2−1
y=x2−3
y=(x−7)2+2
y=−(x+5)2

1. translated 3 units down
2. translated 7 units right and 2 units up
3. reflected over the x-axis, then translated 5 units left
4. vertically stretched by a factor of 2, then translated
4 units left and 1 unit down

Answer 1

1. The given function is

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

The parent function is

`y = {x}^(2)`

The transformation of the form:

`y = f(x - h)`

is a horizontal shift to the right by h units.

where

`f(x) = {x}^(2)`

This implies that:

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

is a horizontal shift to the right by 1 unit.

2) The given function is

`y = 12 {(x + 4)}^(2) - 8`

This also has the parent function to be:

`y = {x}^(2)`

The addition of 4 to x within the parenthesis means a shift of 4 units to the left.

Subtracttion of 8 means a shift of 8 units down.

A multiplier of 12 means a vertical stretch by 12 units.

#1 Translated 4 units left

#2 Shifted 8 units down

#Strectched vertically by a factor of 12

3) We are supposed to match the following functions with the description.

In each case the parent function is

`y = {x}^(2)`

The transformations

`y = - a {(x - b)}^(2) + c`

The negative means a reflection over x-axis.

'a' is a vertical stretch

'b' is a horizontal shift

'c' is a vertical shift.

1) translated 3 units down.

↓

`y = {x}^(2) - 3`

2. Translated 7 units right and 2 units up.

↓

`y = {(x - 7)}^(2) + 2`

3. Reflected over the x-axis , then translated 5 units left

↓

`y = - {(x + 5)}^(2)`

4. Vertically stretched by a factor of 2 , translated 4 units left and 1 unit down.

↓

`y = 2 {(x + 4)}^(2) - 1`