---
title: Forms of a Parabola
---
## Standard Form / General Form

Firstly, let `a`, `b` and `c` represent real numbers that: `a`- is the stretch or compression, `b`- a coefficient of x, and `c`- the y-intercept of the parabola where `a cannot equal 0`.

Standard form (also known as General Form) of a parabola can be represented in the equation below:

y=ax<sup>2</sup>+bx+c

## Factored Form

Firstly, let `a`, `m` and `n` represent real numbers that: `a`- is the stretch or compression, `m` and `n` are the 'zeros' or 'x-intercepts' of the parabola where `a cannot equal 0`. *Please note that not all parabolas can but put into this form.

Factored form of a parabola can be represented in the equation below:

y=a(x-m)(x-n)

## Vertex Form

Firstly, let `a`, `h` and `k` represent real numbers that: `a`- is the stretch of compression, `h` is the x value of the vertex, and `k` is the y value of the vertex. This means that `(h,k)` is the vertex of the parabola. Again `a cannot equal 0`.

Vertex form of a parabola can be representes in the equation below:

y=a(x-h)<sup>2</sup>+k

These are the three forms of a parabola. Remember that `a` will never be 0 because the parabola would automatically become a line, because 0 multiplied by any number is still zero.
