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06 Apr 2019, 22:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
52% (01:22) correct
49%
(01:27)
wrong
based on 200
sessions
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Does the graph of f(x)=ax^2+bx+c have 2 intersections with axis-x?
(1) f(x+2) have 2 intersections with axis-x.
(2) f(x)+2 have 2 intersections with axis-x.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
(1) f(x+2) have 2 intersections with axis-x.
(2) f(x)+2 have 2 intersections with axis-x.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
08 Apr 2019, 22:32
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MBA20
(ax^2+bx+c) graph is a parabola which could look like any of these:
Attachment:
Screenshot 2019-04-09 at 11.00.06.png [ 27.27 KiB | Viewed 3900 times ]
(1) f(x+2) have 2 intersections with axis-x.
The graph of f(x+2) is 2 units to the left of graph of f(x). The graph is exactly the same except it moves 2 units to the left. For example:
Attachment:
Screenshot 2019-04-09 at 10.57.04.png [ 34.4 KiB | Viewed 3864 times ]
Hence this statement alone is sufficient.
(2) f(x)+2 have 2 intersections with axis-x.
f(x) + 2 will be 2 units above the graph of f(x). It is possible that f(x) has two points of intersection too but it is possible that f(x) + 2 is graph B shown in pic above while f(x) is graph A. Hence f(x) may have no point of intersection or 1 point of intersection.
This alone is not sufficient.
Answer (A)
General Discussion
08 Apr 2019, 16:42
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This is quite tricky.
So, we have to deal with a parabola. Let's analyse carefully what the statements tell us:
Statement 1: we know that \(f(x+2)\) have 2 intersections with x-axis. So, for \(x + 2 - 2 = x\), values lie on different places of x-axis, but still are two. Sufficient.
Statement 2: \(f(x) + 2\) means that our parabola is shifted upward by two. If its vertex was located at (0,2), for instance, and \(a < 0\), \(f(x)\) would not meet x-axis at any point. So, insufficient.
So, we have to deal with a parabola. Let's analyse carefully what the statements tell us:
Statement 1: we know that \(f(x+2)\) have 2 intersections with x-axis. So, for \(x + 2 - 2 = x\), values lie on different places of x-axis, but still are two. Sufficient.
Statement 2: \(f(x) + 2\) means that our parabola is shifted upward by two. If its vertex was located at (0,2), for instance, and \(a < 0\), \(f(x)\) would not meet x-axis at any point. So, insufficient.
