describe how the graph of y=x^2 can be transformed to the graph of the given equation y=x^2-20

We can transform this function by adding a constant to the original equation y=x^2. A new transformed function g(x) is given by g(x)=f(x)+c (where f(x)=y)

c>0 moves it up

c<0 moves it down

So: y=x^2+c

y=x^2-20

The new graph will be 20 units down the original.

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luisejr77 luisejr77 · Answer 2 · 2019-08-12T22:06:31+02:00

Answer: The graph of the equation [tex]y=x^2[/tex] can be transformed to the graph of the equation [tex]y=x^2-20[/tex] by shifting [tex]y=x^2[/tex] 20 units downward.

Step-by-step explanation:

Some transformations for a function f(x):

If [tex]f(x)+k[/tex], the function is shifted "k" units upward.

If [tex]f(x)-k[/tex], the function is shifted "k" units downward.

Knowing these transformations and given these equations:

[tex]y=x^2[/tex] and [tex]y=x^2-20[/tex]

We can concluse that the graph of the equation [tex]y=x^2[/tex] can be transformed to the graph of the equation [tex]y=x^2-20[/tex] by shifting [tex]y=x^2[/tex] 20 units downward.