How to Solve Quadratic Equations Using the Quadratic Formula
Master ax² + bx + c = 0, calculate the discriminant (b² - 4ac) to determine real vs complex roots, and solve any quadratic equation.
The Quadratic Formula
x
=
−b ± √(b2 − 4ac)
2a
The Roots of a Quadratic Equation are the X-Intercepts Where the Curve Crosses Zero
The Role of the Discriminant (Δ = b2 − 4ac)
| Discriminant Value | Number of Real Solutions | Parabola Graph Behavior |
|---|---|---|
| Δ > 0 (Positive) | Two distinct real roots | Crosses x-axis twice |
| Δ = 0 (Zero) | One real double root (−b2a) | Vertex touches x-axis exactly once |
| Δ < 0 (Negative) | Two complex conjugate roots (a ± bi) | Floats above or below x-axis (no real intercepts) |
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Your Turn!
Score: 0 / 3Check Your Understanding (3 Quick Questions)
Question 1: In standard form ax² + bx + c = 0, what is b² – 4ac called?
Question 2: If the discriminant Δ < 0 (negative), what roots exist?
Question 3: Solve x² – 5x + 6 = 0:
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