Factored Form
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Factored form of a quadratic expression refers to a way of writing a quadratic equation as the product of two binomials. It is typically written as:
y = a(x - r1)(x - r2)
where:
a is a constant that affects the "stretch" or "compression" of the graph.
r1 and r2 are the roots or solutions of the quadratic equation (the x-intercepts of the graph), meaning the values of x where the equation equals zero.
Factored form is useful because it directly shows the solutions of the quadratic equation (the values of x that make the expression equal to zero) and makes it easier to graph or solve the equation.
Example:
For the quadratic equation y = x^2 -5x + 6, the factored form would be:
y = (x-2)(x-3)
Here, r1 = 2 and r2 = 3, and the factored form shows that the quadratic crosses the x-axis at x = 2 and x = 3.