For f(x) = x2 and g(x) = (x − 4)2, in which direction and by how many units should f(x) be shifted to obtain g(x)?
Left 4 units
Up 4 units
Right 4 units
Down 4 units

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- help_people

- jamiebookeater

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- anonymous

for a function
\[f(x)\]
We have the following ways of how the graph moves
\[f(x+a)\]
Moves the graph LEFT by a units
\[f(x-a)\]
moves the graph RIGHT by a units
\[f(x)+a\]
moves the graph UP by a units
\[f(x)-a\]
moves the graph DOWN by a units,
so what do you think?

- Jhannybean

If you think about it as a parabolic function in vertex form, \(y=a(x-h)^2+k\) You can determine that your vertex is at \((4~,~0)\) whereas the vertex of the parent function is \((0~,~0)\). Comparing the two vertexes, you can tell which way your graph has moved, what is the change from \(4\rightarrow 0=~?\)

- help_people

so a ? @Jhannybean and @Nishant_Garg srry my mom called me :/

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- help_people

srrry i was inactive :)

- Jhannybean

a would be \(g(x) =(x+4)^2\)

- help_people

? thats now what nishant said

- Jhannybean

No, @Nishant_Garg gave you the different variations of HOW the graph would move in certain situations.

- Jhannybean

You can also compare the vertices.. and notice how theyve changed.

- Jhannybean

i mean vertexes*

- Jhannybean

|dw:1442689805859:dw|

- Jhannybean

Which way does it LOOK like it's moving?...

- help_people

to the right

- help_people

4 times

- help_people

@Jhannybean so c?

- Jhannybean

Yep

- help_people

ok great thanks :)

- help_people

can i tag you if i have any more questions?

- mathmate

What @Nishant_Garg said is still true, we only have to read with care. This is what he wrote, with line spacings rearranged.
for a function
f(x)
We have the following ways of how the graph moves
f(x+a)
Moves the graph LEFT by a units
f(x−a)
moves the graph RIGHT by a units
f(x)+a
moves the graph UP by a units
f(x)−a
moves the graph DOWN by a units,
so what do you think?

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