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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.

 Dec 29, 2018
 #1
avatar+98102 
+2

x =  2y^2 - 6y + 3

 

The x intercept is easy....let y = 0    and x =  3

 

To find the y intercepts, let x =  0    and we have

 

2y^2 - 6y + 3 =  0

 

Using the quadratic formula, the y intercepts are

 

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

 

 

cool cool cool

 Dec 29, 2018
 #3
avatar+98102 
+2

Oh...I forgot....you wanted a + b + c

 

This  is

 

3  + 3/2 + 3/2  =

 

3 + 3  = 

 

6

 

cool cool cool

CPhill  Dec 29, 2018
 #4
avatar+809 
+1

Thank you! 

mathtoo  Dec 29, 2018
 #2
avatar+809 
+1

Thank you! Do I have to add the x-intercept to it? So, 3 + that value?

 Dec 29, 2018

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