freeCodeCamp/guide/english/mathematics/forms-of-a-parabola/index.md

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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=ax²+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)²+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.