At how many points do the two graphs named as "First Graph" and "Secon

Question

At how many points do the two graphs named as "First Graph" and "Second Graph" intersect?

1) The Equation of the first graph is x^2 + y^2 = 4
2) The second graph is a parabola with Y-Intercept -5

Source:  https://www.GMATinsight.com

stonecold · Answer

Hey Bunuel

Are Parabolic equations part of the GMAT?
I haven't seen any official question on the same.

Best 
Stone

Bunuel · Answer

In OG there is a chapter on coordinate geometry, where parabolas are discussed: https://gmatclub.com/forum/download/file.php?id=36781 "The graph of a quadratic function is called a parabola and always has the shape of the curve above, although it may be upside down or have a greater or lesser width. Note that the roots of the equation f(x) = x^2 − 1 = 0 are x = 1 and x = − 1 ; these coincide with the x-intercepts since x-intercepts are found by setting y = 0 and solving for x. Also, the y-intercept is f( 0) = − 1 because this is the value of y corresponding to x = 0 . For any function f, the x-intercepts are the solutions of the equation f( x) = 0 and the y-intercept is the value f (0) ." Here is an official question on it: https://gmatclub.com/forum/for-what-val ... 11639.html 2017-08-08_1618.png

GMATinsight · Answer

Please refer to official Guide 17 page number 49... You will find mention of parabola which confirms that GMAT expects test talkers to be equipped with basics of parabola.

Screenshot of OG 17 Page 49 attached

Hope this helps!!!

stne · Answer

Hey GMATinsight,

Can we have the official solution to this one ?

GMATinsight · Answer

After combining the two statements, here are two possibilities

Possibility 1: Circle with radius 2 and Green parabola with Y-intercept as -5 and the two graphs intersecting at 4 points

Possibility 2: Circle with radius 2 and Blue parabola with Y-intercept as -5 and the two graphs intersecting at 0 points

Hence no Unique answer about number of intersections.

NOT SUFFICIENT

Answer: option E

kapstone1996 · Answer

Is it safe to say, that right away you should come down to either C or E.

If the first statement you do not know any information about the second graph and the same for the second statement. This leaves only C or E, and then you will have to just know that parabolic could be spread out really far or narrow, so hard to determine.

I choose E, but was more of an educated guess.

CEdward · Answer

Well, to be frank, there was quite a bit of mental gymnastics trying to figure out how to graph

y = √(2-x)(2+x)

What's clear, however, is that y will always be positive (you can't take the square root of a negative number).

The parabola has an intercept of -5, but this could mean an upside down parabola or it could mean a 'regular' parabola. Two cases - one of which intersects, and the other does not.

E is the answer.

bumpbot · Answer

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At how many points do the two graphs named as "First Graph" and "Secon

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