Question

How do you graph this parabola:

Answer 1

I know the answer, I'm just confuseddddddddd

Answer 2

Again?

Answer 3

Ugh it's just it's SO CONFUSING

Answer 4

hint:
we can rewrite your equation, as below:
\[y - 4 = - {\left( {x - 2} \right)^2}\]

Answer 5

so if we make this traslation:
\[\left\{ \begin{gathered}
Y = y - 4 \hfill \\
X = x - 2 \hfill \\
\end{gathered} \right.\]

Answer 6

oh ok will it always be like that equation for problems like this?

Answer 7

where XOY is the new system of coordinate, we can write your parabola as follows:
\[Y = - {X^2}\]

Answer 8

yes! We have always to make a traslation of our coordinate system xoy to a new coordinate system XOY

Answer 9

How did you get -X^2?

Answer 10

omg never learned this!

Answer 11

we have to apply that above traslation, namely:
we have to write X in place of x-2, and we have to write Y in place of y-4

Answer 12

ok! what next?

Answer 13

we have to understand where the origin O of the XOY system is located, with respect to the old system xoy

Answer 14

what is O

Answer 15

in order to that, we have to set X=0 and Y=0 into that above equation of traslation.
O is the origin of the XOY coordinate system

Answer 16

@Tony00075309aabbc

Answer 17

oh okay!

Answer 18

what does that mean though? What you said before?

Answer 19

if we set X=0, into the prvious system, we get:
\[x - 2=0\]
and then:
x=2

Answer 20

similarly, if we set Y=0 into the previous system, we get:
\[y - 4 = 0\]
and then:
y=4

Answer 21

will someone tag @Tony00075309aabbc ?

Answer 22

in other words, the origin O of the new coordinate system is located at point (2, 4) with respect to the old coordinate system

Answer 23

@deana99

Answer 24

monster she is already in good hands :)

Answer 25

OMG YES, you're right

Answer 26

:) <3