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Algebra Notes 3 – Quadratic Equations & Factorization
A quadratic equation is an equation in which the highest power of the
variable is two. The general form of a quadratic equation is ax² + bx + c = 0,
where a, b, and c are constants and a is not equal to zero.
One common method of solving quadratic equations is factorization. In
this method, the quadratic expression is written as a product of two factors.
For example, x² - 5x + 6 can be factorized as (x - 2)(x - 3) = 0, giving
solutions x = 2 and x = 3.
When factorization is not possible, the quadratic formula is used. The
formula is x = (-b ± √(b² - 4ac)) / (2a). This formula works for all quadratic
equations.
The discriminant, given by b² - 4ac, helps determine the nature of the
roots. If the discriminant is positive, there are two real solutions. If it is zero,
there is one real solution. If it is negative, there are no real solutions.
Quadratic equations can also be represented graphically. Their graphs
form a curve called a parabola. If the value of a is positive, the parabola
opens upward, and if a is negative, it opens downward.
