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Transcript

Ethan Tsea

How exactly does the 90 degree rotation

take place? As we can see in the rotated

equations, "y" does not become the answer, but rather a part of the answer, having to be added

to x on the left side, and having x subtracted

from it on the right side. We can see that the

result of these new equations which have been

rotated, equal to their translation of up and

down on the "x" axis. There are several ways

we can write this however - if we look at the

bright blue line, we can see the equation is:

"-y^2+x=2". This is the equivalent of having:

y^2-x = -2. Again, the -2 clearly indicates that

the line has moved 2 units down on the x axis.

Henry

Chan

Vlado Vasile

We can see from the

graph that the changes

which have taken place

are tobe found when

y=x^2 rotates 90 degrees,

this is the main idea, the

main concept that this

exercise has taught,

because the translation

and reflection we have

previously learnt.

Parabolic

Functions

Here, we have a proof of how this works -

when we rotate y=x^2, what we are actually

doing is reflecting it in "y=x", therefore

instantly creating: y^2-x=0 on GeoGebra.

In order to prove this, we have taken 2

points opposite each other on the lines -

(2,4) and (4,2). If we replaced these numbers

we would have y=x^2 as 4=2^2. In order to

keep this true, the rotated line has to follow

the pattern previously mentioned, so that

we would have: 2^2 - 4 = 0, which works

correctly, because both y and x match up

on both equations.

by Ethan,

and

Vlado

Henry

Vlado Vasile

Thank you!

We can see the exact same

thing here - if we had the

two points, (-4,2) and (-2,4),

and put them into the equation,

y and x would be the same on

both lines - this means we have

found a correct method of this

rotation, and from here on, we

can apply other translations

we have learned, such as

moving the lines up and down,

left and right.

Over this whole Parabolic investigation,

there have been several rules we have

encountered from experimenting with

these lines. With a basic line of y=f(x),

we can change it by doing things like:

Basic:

y = f(x) + a - moves up & down

y = f(x+a) - moves left & right

y=-f(x) - reflects on x axis

y=f(-x) - reflects on y axis

In the future, to extend Parabolic patterns

we could look at things like:

y=a f(x) - Stretches graph parallel to y axis

by a factor

y=f(ax) - Stretches graph parallel to x axis

by a factor

These is a very interesting project with

a lot more we would like to explore.

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