The quadratic formula solves any equation of the form ax² + bx + c = 0.
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y = a·x·x + b·x + c
Reading the quadratic
- The marked roots are the solutions of ax² + bx + c = 0 — where the curve crosses the x-axis.
- The discriminant b² − 4ac counts them: positive ⇒ 2 roots, zero ⇒ 1 (a touch), negative ⇒ none (curve misses the axis).
- The marked vertex sits at x = −b/(2a), midway between the roots.
Your turn
Solve x² − 5x + 6 = 0 with the formula.
Watch out
Don't forget the ± — a quadratic usually has two solutions. And the formula needs the equation set to = 0 first; rearrange before reading off a, b, c.
Quadratic formula
Try it
x² − 5x + 6 = 0
a=1, b=−5, c=6. x = (5 ± √(25−24))/2 = (5±1)/2 = 3 or 2.
The discriminant b² − 4ac tells you how many real roots: positive = 2, zero = 1, negative = 0.