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avatar+1229 

The graph of the parabola \(x = 2y^2 - 6y + 3\) has an x-intercept \((a,0)\) and two y-intercepts \((0,b)\) and \((0,c)\). Find \(a + b + c\).

 Jul 15, 2019
 #1
avatar+103999 
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x  = 2y^2 - 6y  + 3

 

The x intercept is easy....let y  = 0   and the x intercept is  (3, 0)   = (a, 0)

 

To find the y intercepts.....let x = 0   and solve for y

 

2y^2 - 6y +  3 = 0

 

Use the quadratic formula

 

y  =     6 ±√[ 6^2 - 4*3 * 2 ]             6  ±√ [ 36 - 24]             6 ±√12

          ________________  =    ______________  =   __________

                 2 *2                                      4                              4

 

The sum of these two  roots  = b + c   =    2 (6/4)  =  3

 

So

 

a + ( b + c)   =  3 + (3)   =   6

 

 

cool cool cool

 Jul 15, 2019

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