Question

HELP ASAP.....NO LINKS AND NO TROLLING

the graph of f(x)=x^2 is shown


compare the graph of f(x) with the graph of g(x)=x^2+8

Answer 1

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

Answer 2

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

Explanation:

Transformations

For
`a > 0`

`f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}`

`f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}`

`f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}`

`f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}`

Parent function:
`f(x)=x^2`

Translated 8 units up:
`f(x)+8=x^2+8`

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