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19 Sep 2004, 09:36
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1. If y = x^2 + c is the equation of a curve, does this curve lie completely above the x-axis
a) c > 0
b) (1, 4) is a point on the curve
a) c > 0
b) (1, 4) is a point on the curve
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19 Sep 2004, 10:21
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1. If y = x^2 + c is the equation of a curve, does this curve lie completely above the x-axis
a) c > 0
b) (1, 4) is a point on the curve
The primary requrirement for the curve to lie above the x-axis is that the Value Y is never negative. Lets look at the possible values of x that can make Y negative
a) X < 0 : X being negative does not impact Y because in the equation X is raised to a even power making the result positive. Now the total value of Y depends on C
b) X = 0 : C determines the value of Y
c) X >0 - Clearly no issues here as long as C is not negative enough to make the equation.
Therefore we need to answer if C is + or - number.
The option A clearly tells us that C is +. So that helps
The option B gives us values of X & Y, from which C can be calculated. => C = +3.
Answer: Either one by themselves is enough to solve the probelm
a) c > 0
b) (1, 4) is a point on the curve
The primary requrirement for the curve to lie above the x-axis is that the Value Y is never negative. Lets look at the possible values of x that can make Y negative
a) X < 0 : X being negative does not impact Y because in the equation X is raised to a even power making the result positive. Now the total value of Y depends on C
b) X = 0 : C determines the value of Y
c) X >0 - Clearly no issues here as long as C is not negative enough to make the equation.
Therefore we need to answer if C is + or - number.
The option A clearly tells us that C is +. So that helps
The option B gives us values of X & Y, from which C can be calculated. => C = +3.
Answer: Either one by themselves is enough to solve the probelm
19 Sep 2004, 13:14
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Agree with D.
Statement 1: Y is always positive. Sufficient
Statement 2: c=3 -> Y is always positive. Sufficient
Statement 1: Y is always positive. Sufficient
Statement 2: c=3 -> Y is always positive. Sufficient
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
