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What is the equation of the translated function, g(x), if
f(x) = x2?

g(x) = (x – 4)2 + 6
g(x) = (x + 6)2 – 4
g(x) = (x – 6)2 – 4
g(x) = (x + 4)2 + 6

What is the equation of the translated function gx if fx x2 gx x 42 6 gx x 62 4 gx x 62 4 gx x 42 6 class=

Respuesta :

calculista

we have

[tex]f(x)=x^{2}[/tex]

the vertex is the point [tex](0,0)[/tex]

The vertex of the function g(x) is [tex](-4,6)[/tex]

so

the rule of the translation  of f(x) to g(x) is equal to

[tex](x,y)-------> (x-4,y+6)[/tex]

that means

the translation  is [tex]4[/tex] units to the left and [tex]6[/tex] units up

the equation of g(x) is

[tex]g(x)=(x+4)^{2}+6[/tex]

therefore

the answer is

[tex]g(x)=(x+4)^{2}+6[/tex]

Answer:

Option D- [tex]g(x)=(x+4)^2+6[/tex]

Step-by-step explanation:

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

To find : What is the equation of the translated function, g(x)

Solution :

When we see the attached graph

f(x) vertex point is (0,0)

and g(x) vertex point is (-4,6)

The general form of equation with vertex is [tex]y=a(x-h)^2+k[/tex]

where (h,k) are the vertex.

So, the equation of g(x) form is

[tex]g(x)=(x+4)^2+6[/tex]

Therefore, Option D is correct.

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