1. The given function is
[tex]y = {(x - 1)}^{2} [/tex]
The parent function is
[tex]y = {x}^{2} [/tex]
The transformation of the form:
[tex]y = f(x - h)[/tex]
is a horizontal shift to the right by h units.
where
[tex]f(x) = {x}^{2} [/tex]
This implies that:
[tex]y = {(x - 1)}^{2} [/tex]
is a horizontal shift to the right by 1 unit.
2) The given function is
[tex]y = 12 {(x + 4)}^{2} - 8[/tex]
This also has the parent function to be:
[tex]y = {x}^{2} [/tex]
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
[tex]y = {x}^{2} [/tex]
The transformations
[tex]y = - a {(x - b)}^{2} + c[/tex]
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.
↓
[tex]y = {x}^{2} - 3[/tex]
2. Translated 7 units right and 2 units up.
↓
[tex]y = {(x - 7)}^{2} + 2[/tex]
3. Reflected over the x-axis , then translated 5 units left
↓
[tex]y = - {(x + 5)}^{2} [/tex]
4. Vertically stretched by a factor of 2 , translated 4 units left and 1 unit down.
↓
[tex]y = 2 {(x + 4)}^{2} - 1[/tex]
