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Does the curve f(x)=y=ax^2+c intersect with the x - axis?

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Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 08 Mar 2019, 07:56
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A
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Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0
Spoiler: OA
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Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 09 Mar 2019, 07:14
5
I. f(4) > 0
It means a part of the curve is above the x axis at x = 4. But, No info whether
a) the curve is above the x axis
Image
or

b) intersect it in more points.
Image
So, NOT SUFFICIENT.

II. a < 0
It means the parabola, extends downwards but 2 cases are possible.
a) it can intersects
Image
or
b) does not intersect the x axis.
Image

So, NOT SUFFICIENT.

Combing Statement 1 & 2, We get a part of the curve is above the x axis and it extends downwards.
So, It must intersects the x axis.
Image
Hence SUFFICIENT

So, Answer is C


II. a < 0
kiran120680 wrote:
Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0


Spoiler: ::
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Spoiler: ::
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Spoiler: ::
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2A.jpg [ 10.34 KiB | Viewed 1541 times ]

Spoiler: ::
Attachment:
1A.jpg
1A.jpg [ 10.42 KiB | Viewed 1539 times ]

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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 09 Mar 2019, 06:53
kiran120680 wrote:
Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0


Could anyone help with the solution?

Thanks in advance.
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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 09 Mar 2019, 11:24
Thank you gmatbusters!
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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 11 Mar 2019, 23:16
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Algebraic approach
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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 11 Mar 2019, 23:27
Algebraic solution attached. Similar to what gmatbusters has outlined.
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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 07 Aug 2019, 02:16
chetan2u VeritasKarishma Bunuel, could you help with the reasoning for this, please?

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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 07 Aug 2019, 02:17
gmatbusters can u help in clarifying how did u get c as some positive value?

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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

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New post 07 Aug 2019, 21:58
1
kiran120680 wrote:
Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0


y = ax^2 + c is a quadratic so its graph will be a parabola.

I. f(4) > 0
This means when x = 4, y > 0. So at x = 4, the graph lies above the x axis. It can be done in many ways as shown.

Attachment:
IMG_1843.JPG
IMG_1843.JPG [ 2.5 MiB | Viewed 840 times ]


II. a < 0
This means that ax^2 is negative so graph is downward opening. Again, it can be done in many ways as shown.
Attachment:
IMG_3399.JPG
IMG_3399.JPG [ 2.82 MiB | Viewed 841 times ]


Using both, it should lie above x axis at x = 4 but should be downward opening. Hence, only one case is possible. (No 3 in first diagram and no 1 in second diagram, both same)

So the graph will cut x axis.

Answer (C)
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Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?   [#permalink] 07 Aug 2019, 21:58
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Does the curve f(x)=y=ax^2+c intersect with the x - axis?

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