Translation of parabolas
In this Geogebra activity, we are studying the effect of geometric transformations on the graph of a function, in this case, .
This graph is usually called "parabola"
Vertical translation
In the graph below, we have two functions graphed:
- , where
Visualization of a vertical translation
Effect of parameter k
If , what happens to the graph of the function? If , what happens to the graph of the function?
Algebraic expression
Write down the algebraic expression of g(x) in terms of f(x). (Hint: We want an equation between g(x) and f(x))
Horizontal translation
In the graph below, we have two functions graphed:
- , where
Visualization of a horizontal translation.
Effect of parameter h
Algebraic expression
Write down the algebraic expression of g(x) in terms of f(x). (Hint: We want an equation between g(x) and f(x))