Editing Quadratic formula (section)

==Geometric significance==
In terms of coordinate geometry, an axis-aligned parabola is a curve whose {{tmath|(x, y)}}-coordinates are the [[graph of a function|graph]] of a second-degree polynomial, of the form {{tmath|1=\textstyle y = ax^2 + bx + c}}, where {{tmath|a}}, {{tmath|b}}, and {{tmath|c}} are real-valued constant coefficients with {{tmath|a \neq 0}}.

Geometrically, the quadratic formula defines the points {{tmath|(x, 0)}} on the graph, where the parabola crosses the {{tmath|x}}-axis. Furthermore, it can be separated into two terms,

<math display=block>
x = \frac{-b\pm\sqrt{b^2 - 4ac }}{2a}
= -\frac{b}{2a} \pm \frac{\sqrt{b^2 - 4ac}}{2a}.
</math>

The first term describes the [[axis of symmetry]], the line {{tmath|1= x = -\tfrac{b}{2a} }}. The second term, {{tmath|\textstyle \sqrt{b^2 - 4ac}\big/ 2a}}, gives the distance the roots are away from the axis of symmetry.

If the parabola's vertex is on the {{tmath|x}}-axis, then the corresponding equation has a single repeated root on the line of symmetry, and this distance term is zero; algebraically, the discriminant {{tmath|1=\textstyle b^2 - 4ac = 0}}.

If the discriminant is positive, then the vertex is not on the {{tmath|x}}-axis but the parabola opens in the direction of the {{tmath|x}}-axis, crossing it twice, so the corresponding equation has two real roots. If the discriminant is negative, then the parabola opens in the opposite direction, never crossing the {{tmath|x}}-axis, and the equation has no real roots; in this case the two complex-valued roots will be [[complex conjugate]]s whose real part is the {{tmath|x}} value of the axis of symmetry.