Respuesta :

Convert g(x) to vertex form

  • y=x²+8
  • y=(x-0)²+8

Vertex at (0,8)

  • f(x) has vertex (0,0)

Hence

  • f(x) is translated 8 units up

Option D

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Answer:

D.  The graph of g(x) is 8 units above the graph of f(x)

Step-by-step explanation:

Transformations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function: [tex]f(x)=x^2[/tex]

Translated 8 units up:  [tex]f(x)+8=x^2+8[/tex]

Therefore, the graph of g(x) is 8 units above the graph of f(x)

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