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The graph of F(x), shown below, has the same shape as the graph of G(x) = 3x2, but it is shifted down 1 unit. What is its equation? F(x) = _____

A. F(x) = 3(x + 1)2
B. F(x) = 3x2 + 1
C. F(x) = 3x2 - 1
D. F(x) = 3(x - 1)2

Respuesta :

Answer:

[tex]F(x)=3x^2-1[/tex]

Step-by-step explanation:

We have been given the function [tex]G(x)=3x^2[/tex], it is shifted down 1 unit. Now, whenever a function is shifted up or down we just the idea of vertical shift which says:

To shift a function up by 'k' units we use:

[tex]g(x)+k[/tex]

To shift a function down by 'k' units we use:

[tex]g(x)-k[/tex]

Here, in our case we have to shift the function down by 1 unit, so we will subtract 1 from the function:

[tex]F(x)=G(x)-1=3x^2-1[/tex]

So the required function is [tex]3x^2-1[/tex].

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