calling all mathfags /mathematical instinct general/

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Am I right, when I hear "zero" to think "the place where the shapes meet"?

>If this distance term were to decrease to zero, the axis of symmetry would be the x value of the zero, indicating there is only one possible solution to the quadratic equation. Algebraically, this means that √b2 − 4ac = 0, or simply b2 − 4ac = 0 (where the left-hand side is referred to as the discriminant), for its term to be reduced to zero. This is simply one of three cases, where the discriminant can indicate how many zeros the parabola will have. If the discriminant were positive, the distance would be non-zero, and there will be two solutions, as expected. However, there is the case where the discriminant is less than zero, and this indicates the distance will be imaginary — or some multiple of the unit i, such that i = √−1 — and the parabola's zeros will be a complex number. The complex roots will be complex conjugates, and by definition cannot be entirely real, where the real part of the complex root will be the axis of symmetry, therefore geometrical interpretation is that there are no real values of x such that the parabola will be observed to cross the x-axis.