# Vector question confusion

1. Mar 9, 2007

### Trail_Builder

hi, i'm basically a bit confused as to how to solve this vector question, in other words, in what i have to do which is confusing me...

1. The problem statement, all variables and given/known data

This is a sketch of the curve with equation y = f(x)
It passes through the origin O.

(the sketch has no value on or anything, its simply a happy parabola then passes through the origin on the left side a bit of the way up, and dips in the negative y values)

The only vertex of the curve is at A (2, -4)

a) Write down the coordinates of the vertex of the curve with the equation (bold are my answers)

i) y = f(x-3) (5, -4)
ii) y = f(x) -5 (2, -9)
iii) y = -f(x) (2, 4)
iv) y = f(2x) (1, -4)

The curve with equation y=x^2 has been translated to give the curve y=f(x)[/]

b) find f(x) in terms of x

2. Relevant equations

(I dunno if the first half of the question is needed, if it is, say so and ill post it up)

3. The attempt at a solution

not really sure, i know how functions work, I know all about vectors too, but not sure what it means by "translated", and how i would find out the answer.

my instinct says the answer is simply x^2, but somehow I dont think it is, and i certainly dont think that is worthy of 4 marks :S

hope you can help, thnx

i added in the entirity of the question now..

Last edited: Mar 9, 2007
2. Mar 9, 2007

### Dick

Translated how? The question as posted doesn't make much sense. Better post the rest.

3. Mar 9, 2007

### Trail_Builder

ok

ill add it to the main topic

4. Mar 9, 2007

### Trail_Builder

added to the topic the entirity of the question, hope that helps

5. Mar 9, 2007

### Dick

Ok, so y=f(x) is a parabola going through the origin with a vertex at (2,-4) and you want to find its equation given that its a translation of y=x^2? Well, you want to move it two units right and four units down. Having done part a) you should be able to manage that. What's your guess?

6. Mar 9, 2007

### HallsofIvy

Staff Emeritus
That, together with the fact that it is a "happy" (I like that!) parabola with vertex (2, -4) tells you that y= a(x-2)2- 4 for some positive number a.

7. Mar 10, 2007

### Trail_Builder

o rite, see how the answer is y=f(x-2)+4 now, but one thing i a tad confused on

the a you refer to, thats the stretching and stuff yeh, and just to check, is the reason you came to the conlusion that it has to be 1, because it said y = x^2 is translated. does that term translated refer specificially to it moving not being strechted or whatever?

thnx for the help

8. Mar 10, 2007

### HallsofIvy

Staff Emeritus
Yes, in connection with movement (as opposed to translating a language!) means a movement with no stretching or rotating.

By the way, why did you title this "vector question confusion" (and refer to it as a "vector question" in your post) when there are no vectors involved?

9. Mar 10, 2007

### Trail_Builder

oops haha, yeh i realised what i did

basically, i was stuck writing a vector problem in the topic, but then i figured out what i was doing, then went onto to the next question (this question), and forgot to change the topic title hehe

oops