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happyapple123
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In the xy plane, line P intersects y = x^2 + 3 at how many points? Updated on: 30 May 2020, 01:43
Originally posted by happyapple123 on 29 May 2020, 22:33.
Last edited by Bunuel on 30 May 2020, 01:43, edited 2 times in total.
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C
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59% (01:39) correct 41% (01:37) wrong based on 160 sessions

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In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)

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Side question- how do we find the two roots for y=x2 + 3 given that we can't square root negative 3?

Thanks!
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C
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In the xy plane, line P intersects y = x^2 + 3 at how many points? 29 May 2020, 23:12
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is it y=x^2+3 or y=2x+3 ?
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In the xy plane, line P intersects y = x^2 + 3 at how many points? Updated on: 30 May 2020, 00:14
Originally posted by yashikaaggarwal on 29 May 2020, 23:21.
Last edited by yashikaaggarwal on 30 May 2020, 00:14, edited 1 time in total.
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happyapple123
In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)

Show Spoiler
Side question- how do we find the two roots for y=x2 + 3 given that we can't square root negative 3?

Thanks!
Show more

Solve by putting values of x in equation y=x^2+3
We will get value of y
Plot them in quadrant.
It will be a parabola at the end.

Now statement 1: Line P slope is zero, that means line is parallel to x axis. But we don't know from where its parallel to x axis. (Insufficient)

Statement 2: P passes through (-2,7) but to draw equation of line we need another point on line P (insufficient)

Statement 1&2: slope is zero and it passes through point (-2,7) . so the parallel line is at 7 point distance from x axis. If you plot this straight parallel line and the line drew from y=x^2+3 you will get the point at which they intersect. Which is 2 ( hence both statements together is sufficient)
Answer is C

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In the xy plane, line P intersects y = x^2 + 3 at how many points? 30 May 2020, 00:10
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madgmat2019
is it \(y=x^2+3\) or y=2x+3 ?
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it is \(y=x^2+3\)
this is in the form of a parabola, so not a straight line. (it is not a straight line as you suggested y=2x+3)
So now we know its a parabola, and a straight line with slope 0 will either intersect in 2 places or not intersect at all.

Also yashikaaggarwal , according to me you were also thinking that it will intersect in one place, but IMO it would be 2 or 0.
Let us expand on this,
So the equation of the parabola given is \(y=x^2+3\)..........(i)
and equation of line with slope 0 and passing through (-2,7), y=7..............(ii)
Solving (i) and (ii), we get x=+2, -2
This proves the straight line intersects the parabola in 2 places.

Answer would be C as we need both conditions to know if the straight line intersects the parabola or not.
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In the xy plane, line P intersects y = x^2 + 3 at how many points? 30 May 2020, 00:13
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AnirudhaS
madgmat2019
is it \(y=x^2+3\) or y=2x+3 ?
it is \(y=x^2+3\)
this is in the form of a parabola, so not a straight line. (it is not a straight line as you suggested y=2x+3)
So now we know its a parabola, and a straight line with slope 0 will either intersect in 2 places or not intersect at all.

Also yashikaaggarwal , according to me you were also thinking that it will intersect in one place, but IMO it would be 2 or 0.
Let us expand on this,
So the equation of the parabola given is \(y=x^2+3\)..........(i)
and equation of line with slope 0 and passing through (-2,7), y=7..............(ii)
Solving (i) and (ii), we get x=+2, -2
This proves the straight line intersects the parabola in 2 places.

Answer would be C as we need both conditions to know if the straight line intersects the parabola or not.
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Yea sadly I solved it keeping equation of line in mind, thanks for correcting

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In the xy plane, line P intersects y = x^2 + 3 at how many points? Updated on: 07 Jun 2020, 11:14
Originally posted by ManishaPrepMinds on 30 May 2020, 00:52.
Last edited by ManishaPrepMinds on 07 Jun 2020, 11:14, edited 1 time in total.
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In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)


Thanks

Please find the solution below:
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In the xy plane, line P intersects y = x^2 + 3 at how many points? 30 May 2020, 01:43
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happyapple123
In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)

Show Spoiler
Side question- how do we find the two roots for y=x2 + 3 given that we can't square root negative 3?

Thanks!
Show more

Similar question to practice: https://gmatclub.com/forum/in-the-xy-pl ... 09607.html
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In the xy plane, line P intersects y = x^2 + 3 at how many points? 05 Jun 2023, 21:15
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