Formulas & tables/Mathematics/Quadratic function/Factored form

Factored form

f(x)=a(x−x1)(x−x2)f(x)=a(x-x_1)(x-x_2)

Result unit: — (function value)

What it describes

The form showing the roots (it exists when Δ≥0\Delta\ge 0).

Symbols

aa
coefficient
x1,x2x_1, x_2
roots
xx
argument

Where it comes from

Writing the function through its roots — you immediately see where the parabola crosses the xx-axis. It exists only when Δ≥0\Delta\ge0.

When to use it

When you know the roots; sketching the graph, solving quadratic inequalities.

Example

Write the trinomial x2−5x+6x^2-5x+6 in factored form (x1=2x_1=2, x2=3x_2=3).
Substitutiona=1a=1, x1=2x_1=2, x2=3x_2=3.
Resultf(x)=(x−2)(x−3)f(x)=(x-2)(x-3).

Related formulas

Roots (zeros) Vieta's formulas

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