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# In the xy-plane, does y=a(x-k)^2+p intersect with x-axis?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6629
GMAT 1: 760 Q51 V42
GPA: 3.82
In the xy-plane, does y=a(x-k)^2+p intersect with x-axis?  [#permalink]

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Updated on: 11 May 2016, 19:35
1
2
00:00

Difficulty:

75% (hard)

Question Stats:

47% (01:42) correct 53% (01:49) wrong based on 79 sessions

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In the xy-plane, does y=a(x-k)^2+p intersect with x-axis?
1) a<0
2) p>0

* A solution will be posted in two days.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 10 May 2016, 18:03. Last edited by MathRevolution on 11 May 2016, 19:35, edited 1 time in total. Magoosh GMAT Instructor Joined: 28 Dec 2011 Posts: 4489 Re: In the xy-plane, does y=a(x-k)^2+p intersect with x-axis? [#permalink] ### Show Tags 11 May 2016, 13:24 3 MathRevolution wrote: In the xy-plane, does y=a(x-k)2+p intersect with x-axis? 1) a<0 2) p>0 * A solution will be posted in two days. Dear MathRevolution, Just a question of clarification. By y=a(x-k)2+p Do you mean $$y = a(x-k)^2+p$$ Whether the 2 is intended as an exponent is not completely clear. Mike _________________ Mike McGarry Magoosh Test Prep Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6629 GMAT 1: 760 Q51 V42 GPA: 3.82 In the xy-plane, does y=a(x-k)^2+p intersect with x-axis? [#permalink] ### Show Tags 13 May 2016, 03:54 In the original condition, there are 3 variables (a,k and p). In order to match the number of equations to the number of variables, we need 3 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that E is the correct answer. Using the condition 1) and the condition 2) at the same time, we get a diagram like the one attached. If we look at the diagram, the graph passes through (k,p). As p>0, the graph intersects with x-axis. The answer is yes and the condition is sufficient. Hence, the correct answer is C. - Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Attachments 1.png [ 9.04 KiB | Viewed 1147 times ] _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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In the xy-plane, does y=a(x-k)^2+p intersect with x-axis?  [#permalink]

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21 Oct 2017, 03:32
2
Imo Option C
For intersection with x axis
y=0
$$a{(x-k)}^2$$+p=0
$$a{(x-k)}^2$$=$$\frac{-p}{a}$$
We need to the signs of both p&a
From Both statements $$\frac{-p}{a}$$>0
Please give me kudos. I need them badly to unlock gmatclub tests
In the xy-plane, does y=a(x-k)^2+p intersect with x-axis? &nbs [#permalink] 21 Oct 2017, 03:32
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