Question

how do you shift (translate) a quadratic up, down, left or right?

Answer 1

I am going to show on another function, that is a cube root of x.

\(\large\color{ blue }{\large {\bbox[5pt, lightyellow ,border:2px solid white ]{ \large\text{ }\\
\begin{array}{|c|c|c|c|}
\hline~~~~~~~~~~~~~~~~~~~~~~~~~~~\textbf{Shifts}~~~~~~~~~~~~~~~~~~~~~~~~~~~&~\bf{c~~~units~~~~} \\
\hline
\\f(x)= ∛x ~~~ ⇒ ~~~ f(x)= \sqrt[3]{x \normalsize\color{red }{ -~\rm{c}} } &~\rm{to~~the~~right~} \\
\text{ } \\
f(x)= ∛x ~~~ ⇒ ~~~ f(x)= \sqrt[3]{x \normalsize\color{red}{ +~\rm{c}} } &~\rm{to~~the~~left ~} \\
\text{ } \\
f(x)= ∛x ~~~ ⇒ ~~~ f(x)= ∛x \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\
\text{ } \\
f(x)= ∛x ~~~ ⇒ ~~~ f(x)= ∛x \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\
\hline
\end{array} }}}\)

Answer 2

Let's say the parent function is f(x) = x^2. You shift it up or down with a certain number b, like this:

f(x) = x^2 + b.

To shift down, b is negative. To shift up, b is positive. Notice that b is not in parentheses.
Now let's deal with horizontal shifts. To do this, we use a certain number, c. It looks like this:

f(x) = (x-c)^2

Two things to note: If you shift to the right, c is positive. If you shift to the left, c is negative. So against what it may seem like, as long as it's x minus something, it's a shift to the right.
Take a look at this equation:

f(x) = (x-c)^2 + b

This is a combination of the two. The parent function, f(x) = x^2, has been shifted b units up and c units to the right.

Answer 3

inside brackets is translation( left or right) outside brackets is transformation( up or down)

Answer 4

Im too lazy to LaTeX it out. -.-

Answer 5

yes, Lion.k I tried to use that explanation, but seemingly people don't get it....

Answer 6

well if people don't get THAT explanation then ... they should run to google! ;)

Answer 7

It takes a while to really get used to though... When I first learned it I was like wat wat wat too.

Answer 8

SHIFTS:

f(x)= x² ⇒ f(x)= (x \(\normalsize\color{blue}{ +~\rm{c} }\) )² , c units left.
f(x)= x² ⇒ f(x)= (x \(\normalsize\color{blue}{ -~\rm{c} }\) )² , c units right.
f(x)= x² ⇒ f(x)= x² \(\normalsize\color{blue}{ -~\rm{c} }\) , c units down.
f(x)= x² ⇒ f(x)= x² \(\normalsize\color{blue}{ +~\rm{c} }\) , c units up.

Answer 9

what you posted above is the best way! @SolomonZelman

Answer 10

The chart you mean ?

Answer 11

ohh. I see, just this blue Cs ...

Answer 12

yes the chart. Nice!

Answer 13

I combined the latex for box, chart and different colors....I actually tried a chess board, but it is very time-taking and difficult.

Answer 14

I'm not the type to do programming.

Answer 15

me niether

Answer 16

...that's ironic

Answer 17

no really, I am not very good with comps... but I'm okay.

Answer 18

haha! i'm new so i dont even know how to draw matrices. but hopefully people like you can help others very well.
hope you understand @paulvinson

Answer 19

Was about to type something up... but got disconnected... ~