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04 Jan 2021, 09:04
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
53% (01:19) correct
47%
(01:24)
wrong
based on 68
sessions
History
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Time
Result
Not Attempted Yet
In an xy-plane, how many points are common to the x-axis and the curve defined by y = x^2 + bx + c ?
(1 b < 0.
(2) c < 0.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1 b < 0.
(2) c < 0.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
04 Jan 2021, 09:33
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See the imaged attatched for my explanation. OA is B. If you find my post helpful, please give me kudos!
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31 Jan 2021, 01:18
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How many points are “common to the X axis and the curve” essentially means how many times will the parabola cross and intersect the X Axis
By finding the points for X Values that make Y = 0, we will find the X Intercepts.
Setting the Quadratic equal to 0 and solving for the Solutions for X will let us know how many times the parabola intersects the X-Axis.
By using the Discriminant (the value under the square root sign in the quadratic formula) we can see how many times the parabola will cross the X Axis
If: (b)^2 - 4ac = 0 ———- will cross X Axis 1 Time
If: (b)^2 - 4ac > 0 ———— will cross X Axis 2 Times
If: (b)^2 - 4ac < 0 ————- the parabola will never cross the X Axis
S1: just knowing that b is negative does not tell us which of the 3 cases we have. It can be any of the above.
NOT Sufficient.
S2: c < 0
Given that the coefficient for A in front of (x)^2 is equal to 1, we have:
(b)^2 - 4 (1) (- negative value)
The result of the Discriminant will always be Positive and we know that the Parabola will cross the X Axis 2 Times
B s2 alone sufficient
Posted from my mobile device
By finding the points for X Values that make Y = 0, we will find the X Intercepts.
Setting the Quadratic equal to 0 and solving for the Solutions for X will let us know how many times the parabola intersects the X-Axis.
By using the Discriminant (the value under the square root sign in the quadratic formula) we can see how many times the parabola will cross the X Axis
If: (b)^2 - 4ac = 0 ———- will cross X Axis 1 Time
If: (b)^2 - 4ac > 0 ———— will cross X Axis 2 Times
If: (b)^2 - 4ac < 0 ————- the parabola will never cross the X Axis
S1: just knowing that b is negative does not tell us which of the 3 cases we have. It can be any of the above.
NOT Sufficient.
S2: c < 0
Given that the coefficient for A in front of (x)^2 is equal to 1, we have:
(b)^2 - 4 (1) (- negative value)
The result of the Discriminant will always be Positive and we know that the Parabola will cross the X Axis 2 Times
B s2 alone sufficient
Posted from my mobile device
