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

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  6

Step-by-step explanation:

The sum of the roots (y-intercepts) of the polynomial is the opposite of the ratio of the linear term coefficient and the leading coefficient.

  b + c = -(-6/2) = 3

The x-intercept is the constant: a = 3

Then the sum a+b+c is ...

  a + (b +c) = 3 + 3 = 6

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Additional comment

The factored form of the polynomial for the given intercepts will be ...

  x = 2(y -b)(y -c)

and the expanded form of that is ...

  x = 2y^2 -2(b+c)y +2bc

The y-coefficient is ...

  -2(b+c) = -6

  b +c = 3 . . . . . . . divide by -2. This is the result used above.

We show the graph so you can add up the values of the intercepts to see that the sum is 6.