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Geometric transformation 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))

Visualization of a horizontal translation.

Effect of parameter h

  • 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))