Quadratics

A quadratic expression has the form $ax^2 + bx + c$, where $a \neq 0$. A quadratic equation sets this expression equal to zero: $ax^2 + bx + c = 0$. The solutions to this equation are called the roots.

Important properties

• Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula.

• The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

• The discriminant $D = b^2 - 4ac$ tells us how many real solutions there are.

• The graph of a quadratic is a parabola, opening upwards if $a > 0$ and downwards if $a < 0$.