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

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

Direction of the Graph	Opens upward when $a>0$
	Opens downward when $a<0$
$y\text{-}$intercept	$c$
Axis of Symmetry	$x=\text{-}\frac{b}{2a}$
Vertex	$\left(\text{-}\frac{b}{2a},f\left(\text{-}\frac{b}{2a}\right)\right)$

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. 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.

Rewriting a Quadratic Function in Standard Form

Both the vertex and intercept forms of a quadratic function can always be rewritten 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 (also called Factored Form)	$y=a(x-p)(x-q)$	Multiply $a(x-p)(x-q)$ and combine like terms.