Quadratic trinomial

A quadratic trinomial is a second-degree polynomial in one variable, written as $ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers and $a \neq 0$. The graph of a quadratic trinomial is a parabola.

Important properties

• The coefficient $a$ determines if the parabola opens up ($a > 0$) or down ($a < 0$).

• The roots (solutions) of $ax^2 + bx + c = 0$ can be found using factoring, completing the square, or the quadratic formula.

• The vertex of the parabola is at $x = -\frac{b}{2a}$.

• The axis of symmetry is the vertical line $x = -\frac{b}{2a}$.