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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, 08:56
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:39) correct 48% (01:46) wrong based on 31 sessions

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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
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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, 08:14
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


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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, 07:53
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, 12:24
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 12 Mar 2019, 00:16
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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 12 Mar 2019, 00:27
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] 12 Mar 2019, 00:27
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