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.

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

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

This is

3 + 3/2 + 3/2 =

3 + 3 =

6

Thank you!

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