Introduction to Quadratics
Understand what a quadratic equation is and its standard form.
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Introduction to Quadratic Equations
A quadratic equation is any equation that can be written in the form:
$ax^2 + bx + c = 0$
where $a \neq 0$.
📌 Key Terms
- a — the coefficient of $x^2$
- b — the coefficient of $x$
- c — the constant term
- Roots/Zeros — the values of x that make the equation true
Examples of Quadratic Equations
| Equation | a | b | c |
|---|---|---|---|
| $x^2 - 5x + 6 = 0$ | 1 | -5 | 6 |
| $2x^2 + 3x - 1 = 0$ | 2 | 3 | -1 |
| $x^2 = 4$ | 1 | 0 | -4 |
The Discriminant
The discriminant tells us how many real roots a quadratic has:
$\Delta = b^2 - 4ac$
| Discriminant | Number of Real Roots |
|---|---|
| $\Delta > 0$ | Two distinct real roots |
| $\Delta = 0$ | One repeated root |
| $\Delta < 0$ | No real roots |
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Quadratic Equations
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