Finding the Vertex of a Translated Curve

[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...

Homework Statement

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

Homework Equations

(I don't know if the first half of the question is needed, if it is, say so and ill post it up)

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 don't think it is, and i certainly don't think that is worthy of 4 marks :S


hope you can help, thnx


i added in the entirity of the question now..

 

[Dick]

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

 

[Trail_Builder]

ok

ill add it to the main topic

 

[Trail_Builder]

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

 

[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?

 

[HallsofIvy]

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...

Homework Statement

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)

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.

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)[/]
Okay, that tells you that the "a" above is 1!

b) find f(x) in terms of x
From the first statement, that this is a parabola opening upward with vertex (2, 4), you know the equation is y= a(x-2)²+ 4. Now you know that a= 1!

Homework Equations

(I don't know if the first half of the question is needed, if it is, say so and ill post it up)

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 don't think it is, and i certainly don't think that is worthy of 4 marks :S


hope you can help, thnx


i added in the entirity of the question now..

 

[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, that's 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

 

[HallsofIvy]

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?

 

[Trail_Builder]

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?

oops haha, yeh i realized 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