What is a Translation? A translation moves the graph up, down, and side to side. [br][br]What is a Dilation? A dilation makes the function skinnier or larger. [br][br]What is a Reflection? A reflection is a mirror image. This flips the function over the x or y axes.[br][br]What is a Rotation? It depends on the type of line but a rotation is when the function is rotated about some axis by some degree. [br]
Why do you think we do the opposite motion when the function translates along the x axis? [br][br]Hint: Look at [math]\left(x-h\right)^2[/math]. Notice that when the graph moves along the positive x direction the function looks like (x - h) but when the function moves in the negative x direction the function looks like (x + h). Why do you think this happens?
-When we derive the vertex formula of a parabola from its standard form the formula works out so that the formula is (x-h)^2 plus some k.