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y=2x^2+x-5
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13 Mar 2024, 23:11
13 Mar 2024, 23:11
Expert Reply
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Question Stats:
50% (02:55) correct
50% (02:19) wrong based on 8 sessions
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\(y=2x^2+x-5\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The distance between the y intercept and the value of x at the line of symmetry |
The distance between the x intercepts |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
y=2x^2+x-5
[#permalink]
12 Apr 2024, 10:22
12 Apr 2024, 10:22
Expert Reply
Actually we are dealing with a parabola
Using the distance formula
\(x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)
\(x= \dfrac{-1 b \pm \sqrt{1^2-425*-5c}}{2*2}\)
\(x=-\frac{1}{4} \pm \dfrac{\sqrt{41}}{4}\)
The line of symmetry in the equation is namely -1/4
For quantity B the intercept is
\(x_1=-\frac{1}{4} + \dfrac{\sqrt{41}}{4}\)
\(x_2=-\frac{1}{4} - \dfrac{\sqrt{41}}{4}\)
Now the distance between the two points
\(|x_1-x_2|\)
\(|( \dfrac{-1}{4}+ \dfrac{\sqrt{41}}{4}) - (\dfrac{-1}{4}- \dfrac{\sqrt{41}}{4})|\)
\(| \dfrac{\sqrt{41}}{4}+ \dfrac{\sqrt{41}}{4}|=3.2\)
B is the answer
Using the distance formula
\(x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)
\(x= \dfrac{-1 b \pm \sqrt{1^2-425*-5c}}{2*2}\)
\(x=-\frac{1}{4} \pm \dfrac{\sqrt{41}}{4}\)
The line of symmetry in the equation is namely -1/4
For quantity B the intercept is
\(x_1=-\frac{1}{4} + \dfrac{\sqrt{41}}{4}\)
\(x_2=-\frac{1}{4} - \dfrac{\sqrt{41}}{4}\)
Now the distance between the two points
\(|x_1-x_2|\)
\(|( \dfrac{-1}{4}+ \dfrac{\sqrt{41}}{4}) - (\dfrac{-1}{4}- \dfrac{\sqrt{41}}{4})|\)
\(| \dfrac{\sqrt{41}}{4}+ \dfrac{\sqrt{41}}{4}|=3.2\)
B is the answer
gmatclubot
y=2x^2+x-5 [#permalink]
12 Apr 2024, 10:22
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