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15 Sep 2021, 05:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:15) correct
27%
(01:21)
wrong
based on 139
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In the xy-plane, at what two points does the graph of y = (x - k)(x + k) intersect the x-axis?
(1) k^2 = 9
(2) k = 3
(1) k^2 = 9
(2) k = 3
15 Sep 2021, 06:19
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Bunuel
Target question: At what two points does the graph of y = (x - k)(x + k) intersect the x-axis?
Key property: When a line or curve crosses the x-axis, the coordinates of the point(s) of intersection are in the form (x, 0). In other words, the y-coordinate at the point of intersection is 0
Statement 1: k^2 = 9
This tells us that EITHER k = 3 OR k = 3.
Let's consider each possible case:
Case a: k = 3. In this case, the equation becomes y = (x - 3)(x + 3), which means the graph intersects the x-axis at (3,0) and (-3,0).
Case b: k = -3. In this case, the equation becomes y = (x - (-3))(x + (-3)), which is the same as the equation y = (x + 3)(x - 3). Here, the graph intersects the x-axis at (-3,0) and (3,0).
So, for both possible cases, we get the same answer to the target question: the graph intersects the x-axis at (3,0) and (-3,0).
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: k = 3
In this case, the equation becomes y = (x - 3)(x + 3), which means the graph intersects the x-axis at (3,0) and (-3,0).
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
18 Sep 2021, 08:09
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Bunuel
They intersect the x-axis at k and -k. So we only need to find k.
Statement 1:
k = 3 or -3. In either case, however, the intersections are x = 3 and x = -3. Therefore this is sufficient.
Statement 2:
Sufficient.
Ans: D
