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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
Date
Time
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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.
(1 b < 0.
(2) c < 0.
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
