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If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max

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Carcass
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If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   Updated on: 07 Aug 2025, 11:08
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If \(y = -x^2 + 1\) intersects line \(k\) at \((t, -3)\) and \((p, 0)\), what is the maximum possible slope for line \(k\)?

(A) -3
(B) 2
(C) 3
(D) 4
(E) 9
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C

Originally posted by Carcass on 06 Feb 2022, 06:00.
Last edited by Carcass on 07 Aug 2025, 11:08, edited 2 times in total.
Fixed typo
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KarunMendiratta
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   24 Feb 2022, 23:22
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Carcass wrote:
If \(y = -x^2 + 1\) intersects line k at (t, 3) and (p, 0), what is the maximum possible slope for line k?

(A) -3
(B) 2
(C) 3
(D) 4
(E) 9


Graph of \(y = -x^2 + 1\) will never have y = 3 as its maximum (vertex) lies at (0,1)
Carcass Can you please check?
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   24 Feb 2022, 23:54
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KarunMendiratta wrote:
Carcass wrote:
If \(y = -x^2 + 1\) intersects line k at (t, 3) and (p, 0), what is the maximum possible slope for line k?

(A) -3
(B) 2
(C) 3
(D) 4
(E) 9


Graph of \(y = -x^2 + 1\) will never have y = 3 as its maximum (vertex) lies at (0,1)
Carcass Can you please check?


Yes sir. sure thing. Both the question and the oA are correct according to the book. However, I do not have the OE for this particular question.
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   05 Nov 2022, 01:45
2
\(y=−x^2+1\)
to get t, substitute the coordinates into the eq
\(-3 = -t^2+1\)
\(t = +-2\)

to get p, substitute the coordinates into the eq
\(0 = -p^2+1\)
\(p = +-1\)

if you draw out the 4 possible points, you will see the max gradient can be obtained with t = -2 and p = -1
gradient \(= (-3-0)/(-2-(-1))\)
= 3, hence the answer is C
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KarunMendiratta
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   07 Nov 2022, 10:42
KarunMendiratta wrote:
Carcass wrote:
If \(y = -x^2 + 1\) intersects line k at (t, 3) and (p, 0), what is the maximum possible slope for line k?

(A) -3
(B) 2
(C) 3
(D) 4
(E) 9


Graph of \(y = -x^2 + 1\) will never have y = 3 as its maximum (vertex) lies at (0,1)
Carcass Can you please check?


Carcass

The stem has been edited I guess!
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   07 Nov 2022, 13:18
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KarunMendiratta wrote:
KarunMendiratta wrote:
Carcass wrote:
If \(y = -x^2 + 1\) intersects line k at (t, 3) and (p, 0), what is the maximum possible slope for line k?

(A) -3
(B) 2
(C) 3
(D) 4
(E) 9


Graph of \(y = -x^2 + 1\) will never have y = 3 as its maximum (vertex) lies at (0,1)
Carcass Can you please check?


Carcass

The stem has been edited I guess!


Fixed sir. Thank you and sorry for the inconvenience.

I edited on my own. I guess the book was wrong

take a look now , please
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   07 Aug 2025, 10:39
karun's pointed out a flaw in this problem and it appears that the stem still has not been fixed. to anyone confused by this problem, the first point should be (t, -3) NOT (t, 3)
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink] New post   07 Aug 2025, 11:09
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I fixed accordingly to your suggestion sir.

The point in that way would never be in the parabola
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Re: If y = -x2 + 1 intersects line k at (t, 3) and (p, 0), what is the max [#permalink]
07 Aug 2025, 11:09
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