The Discriminant: A Parabola's Fate

This tiny part of one math formula can literally predict a graph's future. You know quadratic

functions, the ones that make that U-shape called a parabola? The 'a' value in

the formula, ax² + bx + c, tells you if it opens up or down. The 'c' value is

a cheat code for where it hits the y-axis. But the real secret is the discriminant:

b² - 4ac. If it's positive, your parabola crosses the x-axis twice. If it's zero,

it just kisses it at one point. And if it's negative? It floats forever, never touching.

It's not just a formula; it's the parabola's entire story.