Parabola problem

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jonny9987

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A quadratic function has equation f(x) = kx^2. P and Q are points on the parabola with x-coordinates p and q, respectively. A straight line, parallel to PQ, is drawn from the origin O, to the point R. The x-coordinate of R is r.

Show that r = k(p+q).

Have no idea where I'm going with this, any help would be appreciated.
 
Point \(P\) has the coordinates:

[MATH](p,kp^2)[/MATH]
And point \(Q\) has the coordinates:

[MATH](q,kq^2)[/MATH]
And so what is the slope of \(\overline{PQ}\) ?
 
You really need to draw a diagram!

f(x) = kx^2 is a parabola whose vertex is at (0,0). Assume k>0 so the parabola opens upwards (you an choose k<0 as it will not matter)

Step 1: Draw the parabola
Step 2. Pick 2 points on the parabola. One point P =(p, kp^2) and the other point Q = (q, kq^2). Label them on the graph.

So far all we did is graph/label what was given.

Step 3: Draw the line from P to Q.
Step 4: Draw a line parallel to PQ that goes through the origin.
Now I can only assume that the point R that the problem refers to is on the parabola. Point R is at (r, kr^2).

Step 5: Find the slope of PQ.
Step 6: Armed with this slope and the point (0,0) you can find the equation of the line that goes from the origin to point R.

Step 7: Find the intersection of the parabola and the line.
 
I gave this problem a bit more thought and I do not think that r is in terms of k, p and q but rather that r is only in terms of p and q. That is I think that the conclusion that r=k(p+q) is false.
 
To the OP. I think that r=(p+q) and not r =k(p+q). So you can still try to do the problem.
 
Jomo said:
To the OP. I think that r=(p+q) and not r =k(p+q). So you can still try to do the problem.
Click to expand...

I came to the same conclusion when I worked the problem, to decide how to point the OP in the right direction. I was going to address that by asking if the problem says \(R\) is on the parabola or not once they determined the slope I requested. With no other information, I was left to assume it is on the parabola too, and that the conclusion given is false.
 
[MATH][/MATH][MATH][SUB][/SUB][/MATH]
Hey, thanks for the help. Nah the question doesn't state whether R sits on the parabola... This is what I got in the end. Still kind of confused to be honest.
 

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jonny9987 said:
[MATH][/MATH][MATH][SUB][/SUB][/MATH]
Hey, thanks for the help. Nah the question doesn't state whether R sits on the parabola... This is what I got in the end. Still kind of confused to be honest.
Click to expand...
As far as I can tell, you have solved the problem as intended.

I believe R is supposed to be on the parabola; if they don't say that in words, then I would expect a picture to have shown it.

I also believe they meant to say that r = p+q; that is true is r is on the parabola.

See posts #5 and #6. The problem is bad in at least one way, probably two. Don't waste any more time on it.
 
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