Question

The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of (in red).

The function f is defined by f(x)=x^2 .
Write down the expression for k(x) .

Answer 1

k(x)=?

Answer 2

Okay... I'm not sure how to explain this... it's all in the vertices...
The vertex of the blue graph is (0,0), what's the vertex of k(x) ?

Answer 3

3,2

Answer 4

okay, so, the vertex form of a quadratic equation is
\[\large y = (x-h)^2 +k\]
where (h,k) is the vertex
so in the case where y = x^2
h = 0
and
k = 0

So what about if the vertex is to be on the point (3,2) ?

Answer 5

um..

Answer 6

0?

Answer 7

sry kind of blank.

Answer 8

What are h and k?

Answer 9

?

Answer 10

Read up that major post I put up, with the vertex form, the answer's there :)

Answer 11

0

Answer 12

Wait im confused im sorry. :(

Answer 13

so I do the equation you put there?

Answer 14

Yeah, but fill in the appropriate values for h and k.

Answer 15

which are 0? cause for k its 3,2 so which of the 2 numbers

Answer 16

Like I said, (h,k) is the vertex of the parabola :)

Answer 17

so 0? i still stay like this y=(x-0)^2+k. Sry I dont understand hahaha. I know im taking up your time.

Answer 18

y=(x-0)^2+0*

Answer 19

Yes, that's for the blue parabola when the vertex was (0,0)
but what about the red one?

Answer 20

3,2

Answer 21

right?

Answer 22

but is it on y line or x, which one do i use for the equation? and which are y and x?

Answer 23

My brain is slow after 8 hours of math lol. sry

Answer 24

You're right in saying that the vertex of the red parabola is (3,2) so why don't you go ahead and plug that into the vertex form of the equation?

Answer 25

so y=(x-0)^2+3or2?

Answer 26

Nope.

Answer 27

2=(0-0)^2+3?

Answer 28

man I way of track hahah

Answer 29

You probably need some rest from all this maths.

Answer 30

what is the answer and let me see if i can figure it out pls? ill see if i can tell you how you took it?

Answer 31

Behold...
VERTEX:
\[\Large (\color{red}h,\color{green}k)\]

VERTEX FORM
\[\Large y = (x-\color{red}h)^2 + \color{green}k\]

Answer 32

Just plug in and you'll be done.

Answer 33

im looking for what k(x). and which numbers do I plug in. we got this far last time lol.

Answer 34

You plug in the vertex.
We also got this far last time

Answer 35

which there are 4 (0,0) and (3,2) so i cant plug in all

Answer 36

y=(x-0)^2+3

Answer 37

(0,0) is the vertex of the blue parabola.
(3,2) is the vertex of k(x) (the red one)

Which one is the one that the question asks for? You decide :P

Answer 38

y=(3-0)^2+2?

Answer 39

pls tell me im close. am I?

Answer 40

Not even :D
Leave the x and y alone, it's the h and k that we're interested in.

Answer 41

okay

Answer 42

y=(x-3)^2+2

Answer 43

its that one better?

Answer 44

Much.

Answer 45

but now im missing the x and y...

Answer 46

Meaning...?

Answer 47

i cant solve the equation without the x and y well i can but shoud they stay x and y?

Answer 48

Of course they should stay x and y.... -.-

It's an equation of a parabola... all points that the (red) parabola crosses would satisfy the equation
y = (x - 3)^2 + 2

Just you try plugging in (3,2) for (x,y)

Answer 49

OH OH OH okay okay get it

Answer 50

so 2=(3-3)^2+2?

Answer 51

yes, and it checks out, right?

Answer 52

which is 1

Answer 53

I don't understand... how do you figure 1?

Answer 54

well do the equation and you get 1 no? (3-3)^2=0 so 2/2 =1

Answer 55

did i just go off track?

Answer 56

Well, fine, that does make sense, I guess.

Answer 57

yet i see you arnt convinced? I got it wrong right? again

Answer 58

No, it's not wrong, it just wasn't the way I expected it.

Answer 59

oh lol whats the other way?

Answer 60

Many ways... anyway, that's not important, the important thing is that you've gotten your answer.

Answer 61

Oh thank God! Thanks for the help! sry I know I stressed you up! but, you stayed thanks!!!!

Answer 62

Your equation of the red parabola is the
y = (x - 3)^2 + 2

This can be obtained by the way you just did...OR to make it easier for next time....read up about vertical shifts, horizontal shifts etc...

You could have seen that Adding 2 to the whole expression...shifts a graph up by 2....and subtracting 3 from the (x)² would shift the graph over to the right by 3....

Just read up...but this way was completely logical!

Answer 63

okay thanks

Answer 64

Thanks Terenz!

Answer 65

no problem :)
But please read up, and read thoroughly ~

Answer 66

k