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In the xy-coordinate plane, the graph of y=x^2-kx-6, where

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tr1
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In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  Updated on: 29 Oct 2017, 20:52
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In the xy-coordinate plane, the graph of \(y=x^2-kx-6\), where k is a constant, crosses the x-axis at two points. What is the value of k?

(1) For each of the two points where the graph crosses the x-axis, the x-coordinate is an integer.
(2) The graph crosses the x-axis at (1,0).
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Originally posted by tr1 on 26 Feb 2014, 07:44.
Last edited by Bunuel on 29 Oct 2017, 20:52, edited 2 times in total.
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Bunuel
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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  26 Feb 2014, 08:06
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tr1 wrote:
Hey everybody,

this forum has helped me immensely in analyzing my wrong answers on the GMATprep tests. I have not found an explained answer to this question yet, so here we go:


In the xy-coordinate plane, the graph of \(y=x^2-kx-6\), where k is a constant, crosses the x-axis at two points. What is the value of k?

(1) For each of the two points where the graph crosses the x-axis, the x-coordinate is an integer.
(2) The graph crosses the x-axis at (1,0).

Thanks,
Tim


In the xy-coordinate plane, the graph of \(y=x^2-kx-6\), where k is a constant, crosses the x-axis at two points. What is the value of k?

(1) For each of the two points where the graph crosses the x-axis, the x-coordinate is an integer.

If \(y=(x+2)(x-3)=x^2-x-6\), so if the x-intercepts, are -2 and 3, then k=1;
If \(y=(x-2)(x+3)=x^2+x-6\), so if the x-intercepts are 2 and -3, then k=-1.

Not sufficient.

You could notice that \(y=x^2-kx-6\) can be factored in many ways so that x-intercepts are integers:
\(y=(x+2)(x-3)\),
\(y=(x-2)(x+3)\),
\(y=(x+6)(x-1)\),
\(y=(x-6)(x+1)\),
...

(2) The graph crosses the x-axis at (1,0) --> substitute x=1 and y=0, into the equation: \(0=1^2-k-6\) --> k=-5. Sufficient.

Answer: B.

Factoring Quadratics: https://www.purplemath.com/modules/factquad.htm

Solving Quadratic Equations: https://www.purplemath.com/modules/solvquad.htm

Hope this helps.
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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  26 Feb 2014, 08:17
This clears it up, thanks a lot!
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In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  Updated on: 01 Jun 2019, 10:53
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Edit: useful vocabulary to know ... "crosses the x-axis at..." = "x-intercepts" = "roots" = "solutions" = "zeroes"
https://www.purplemath.com/modules/intrcept.htm

Originally posted by energetics on 01 Jun 2019, 09:19.
Last edited by energetics on 01 Jun 2019, 10:53, edited 1 time in total.
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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  01 Jun 2019, 10:07
I am not sure what you meant.

My two cents ,

But , if a graph is passing through (a,b), then this point will satisfy the graph equation

means if we out x = a and y = b in the original graph equation , then

LHS = RHS

using same logic, here we found the value of K by putting y =0 and x =1 in the original graph equation .


Hope this helps.

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In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  30 Mar 2021, 01:38
Hi Bunuel

why do you removed the K in that calculation in bold, how can I recognize that I have to do so?

Quote:
If y=(x+2)(x−3)=x2−x−6y=(x+2)(x−3)=x2−x−6, so if the x-intercepts, are -2 and 3, then k=1;
If y=(x−2)(x+3)=x2+x−6y=(x−2)(x+3)=x2+x−6, so if the x-intercepts are 2 and -3, then k=-1.



Many thanks :-)
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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  30 Mar 2021, 01:48
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gastoneMIT wrote:
Hi Bunuel

why do you removed the K in that calculation in bold, how can I recognize that I have to do so?

Quote:
If y=(x+2)(x−3)=x2−x−6y=(x+2)(x−3)=x2−x−6, so if the x-intercepts, are -2 and 3, then k=1;
If y=(x−2)(x+3)=x2+x−6y=(x−2)(x+3)=x2+x−6, so if the x-intercepts are 2 and -3, then k=-1.



Many thanks :-)


We need to find the value of k. For (1) the solution above demonstrates that k could take more than one value, which indicates that (1) is not sufficient to find the single numerical value of k. For example, if \(y=(x+2)(x-3)=x^2-x-6\), (the x-intercepts, are integers -2 and 3), then k=1 but if \(y=(x-2)(x+3)=x^2+x-6\), (the x-intercepts are integers 2 and -3), then k=-1.
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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  12 Oct 2021, 23:13
Is this question really sub-600 level? It takes a bit of brian to split and find k's possible values for roots to be integers.
Bunuel any thoughts?
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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  13 Oct 2021, 01:14
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kittle wrote:
Is this question really sub-600 level? It takes a bit of brian to split and find k's possible values for roots to be integers.
Bunuel any thoughts?


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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink] New post  04 Aug 2022, 13:03
In the xy-coordinate plane, the graph of \(y=x^2-kx-6\), where k is a constant, crosses the x-axis at two points. What is the value of k?

(1) For each of the two points where the graph crosses the x-axis, the x-coordinate is an integer.
(2) The graph crosses the x-axis at (1,0).
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Re: In the xy-coordinate plane, the graph of y=x^2-kx-6, where [#permalink]
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