Standard Form of a Quadratic Function

The standard form of a quadratic function is a quadratic function written in a specific format.

$f (x) = a x^{2} + b x + c$

Here, $a,$ $b,$ and $c$ are real numbers with $a \neq = 0 .$ The term with the highest degree — the quadratic term — is written first. Then, the linear term followed by the constant term are written. The standard form can be used to determine the direction of the parabola, the $y -$ intercept, the axis of symmetry, and the vertex.

Standard Form of a Quadratic Equation

Similar to a quadratic function, a quadratic equation can be written in standard form. This is called the standard form of a quadratic equation.

a x^{2} + b x + c = 0

In this equation,

a

is not equal to

0 .

The solutions of a quadratic equation written in this form can be found by applying the Quadratic Formula.

Both the vertex and the intercept form of a quadratic function can always be written in standard form.

Form	Equation	How to Rewrite?
Vertex Form	$y = a (x - h)^{2} + k$	Expand $(x - h)^{2},$ distribute $a,$ and combine like terms.
Intercept Form	$y = a (x - p) (x - q)$	Multiply $a (x - p) (x - q)$ and combine like terms.

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