Transformation
To be able to do this you need to know the basics of graphing.
Equations and their shapes
the following pictures are the shapes and general information that you'd need to know.
Moving The Equation around
MOving the equations up & Down
1.) Adding outside the parent function:It moves it straight up that many spaces
2.) Subtracting outside the parent function: It moves it straight down that many spaces
Examples:
a. y = x2 + 3 b. y = x2 + 2 c. y = x2 - 3 d. y = x2 - 1
2.) Subtracting outside the parent function: It moves it straight down that many spaces
Examples:
a. y = x2 + 3 b. y = x2 + 2 c. y = x2 - 3 d. y = x2 - 1
MOving the equation left & RIght
3.) Adding inside of a parent function : moves it to the left
4.) Subtracting inside of a parent function: moves it to the right
Examples
a. y = (x - 3)2 b. y = (x - 2)2 c. y = (x + 1)2 d. y = (x + 2)2
4.) Subtracting inside of a parent function: moves it to the right
Examples
a. y = (x - 3)2 b. y = (x - 2)2 c. y = (x + 1)2 d. y = (x + 2)2
Stretching & shrinking the Equation
5.) Multiplying by an integer: vertically stretching it (thinner)
6.) Multiplying by a fraction: makes it wider vertically shrunk
Examples
a. y = 2x2 b. y = -3x2 c. y = 1/2x2 d. y = 1/3x2
6.) Multiplying by a fraction: makes it wider vertically shrunk
Examples
a. y = 2x2 b. y = -3x2 c. y = 1/2x2 d. y = 1/3x2
Flipping the equation
If it is negative it flips the equation over the x-axis.
Examples
y=-x^2
Examples
y=-x^2