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Quadratic equation - Parabola

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Quadratic equation - Parabola

by hemanthquartz1 » Sun Jan 17, 2010 3:09 am
Hello Guru's

Please help me solve this question.

1.On the graph When x=1/2,y=2;and when x=1,y=1.The graph is symmetric with respect to the vertical line at x=2.According to the graph,when x=3,y=

a) -1
b)-1/2
c)0
d)1/2
e)1

2. Could you also find out the parabolic equation?

Finding the equation has been driving me crazy for few hours now to . I have used this equation Y=Ax2+Bx+C but not able to solve it. Please help.

Thanks
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by hemanthquartz1 » Sun Jan 17, 2010 6:16 pm
Hello,

I am still waiting for the reply. Could some please try to solve this?
Could someone solve the equation for the points?

Thanks
Hemanth
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by ace_gre » Mon Jan 18, 2010 11:03 pm
Hi, I googled for equation for parabola and found that I need to use one more equation to solve..(axis of symmetry x = -b/2a)

https://www.mathwarehouse.com/geometry/p ... x-form.php

y = ax^2 + bx + c

when x =1/2 , y = 2 ,
8 = a + 2b + 4c--------(1)

when x= 1, y =1,
1= a + b + c-----------(2)

x = 2 = -b / 2a
b = -4a---------------(3)

Multiply (2) by 4 and subtract from (1)

4 = -3a -2b
4= -3a -2(-4a)
4 = 5a
a = 4/5
Substitute a = 4/5 in (3)
b = -16/5

Substitute the above in (1), c= 17/5
Parabola equation y = 4/5 x^2 - 16/5 x + 17/5
when x=3, y =1

IMO E y=1 , parabola equation 5y= 4x^2 - 16x + 17.

Is this correct? Please post OA.
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by hemanthquartz1 » Tue Jan 19, 2010 8:13 am
Thank you so much for the reply and for the link.
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by Brent@GMATPrepNow » Wed Jan 20, 2010 6:49 pm
hemanthquartz1 wrote:Hello Guru's

Please help me solve this question.
1.On the graph When x=1/2,y=2;and when x=1,y=1.The graph is symmetric with respect to the vertical line at x=2.According to the graph,when x=3,y=
a) -1
b)-1/2
c)0
d)1/2
e)1
2. Could you also find out the parabolic equation?
Finding the equation has been driving me crazy for few hours now to . I have used this equation Y=Ax2+Bx+C but not able to solve it. Please help.
Thanks
I can assure you that you don't need to know how to find the equation of a parabola on the GMAT.
The important point to recognize here is that parabolas are symetrical about an axis. See image.
Image
Brent Hanneson - Creator of GMATPrepNow.com
Image
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