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

Question

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

anonymous · Answer

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 · Answer

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 · Answer

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

help_people · Answer

srrry i was inactive :)

jhannybean · Answer

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

help_people · Answer

? thats now what nishant said

jhannybean · Answer

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

jhannybean · Answer

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

jhannybean · Answer

i mean vertexes*

jhannybean · Answer

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