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Transformation Notes
Vertex form of a quadratic equation: 𝒇(𝒙) = 𝒂(𝒙 − 𝒉) + 𝒌
Vertical Shift: When a number is added to the “outside” of the basic parent function.
The parent function will move __________ when you add a positive number.
The parent function will move ____________ when you add a negative number.
Example:
𝒇(𝒙) = 𝒙𝟐
𝒇(𝒙) = 𝒙𝟐 + 𝟑
𝒇(𝒙) = 𝒙𝟐 − 𝟒
Parent Function
Moves
Moves
Horizontal Shift: When a number is added to the “inside” of the basic parent function.
The parent function will move __________ when you add a positive number.
The parent function will move ____________ when you add a negative number.
Example:
𝒇(𝒙) = 𝒙𝟐
𝒇(𝒙) = (𝒙 + 𝟐)𝟐
𝒇(𝒙) = (𝒙 − 𝟔)𝟐
Parent Function
Moves
Moves
Stretch/Shrink: When the basic parent function is multiplied by a number.
The parent function will ________________ when you multiply by a fraction
(a number in between 0 and 1).
The parent function will ____________ when you multiply by a whole number
(a number greater than 1).
Example:
𝒇(𝒙) = 𝒙𝟐
𝒇(𝒙) = 𝟑𝒙𝟐
𝟏
𝒇(𝒙) = 𝟐 𝒙𝟐
Parent Function
Reflection: When basic parent function is multiplied by a negative.
The parent functions will __________ when you multiply by a ____________.
Example:
𝒇(𝒙) = 𝒙𝟐
𝒇(𝒙) = −𝒙𝟐
Parent Function
Putting it all together….
Given the parent function 𝑦 = 𝑥 2 name the transformations
1
1. 𝑦 = − 2 (𝑥 + 7)2
2. 𝑦 = 8(−6 + 𝑥)2 − 3
3. 𝑦 = −(𝑥 − 4)2 + 2
4. 𝑦 = 0.6(𝑥 + 1)2 − 4