Question 48215
Well, the answer is one or both of the above.
If the vertex of the parabola is on the y-axis, then, if the parabola intersects the x-axis, it does so at +x and -x and the coefficient of x (b) is 0.

If the parabola doesn't inersect the x-axis, but the vertex is on the y-axis, then the coefficient of x (b) is 0.

See the graphs below of {{{y = x^2-2}}} (red) and {{{y = x^2+2}}} (green):
{{{graph(300,200,-5,5,-10,10,x^2-2,x^2+2)}}}