29 lines
1.2 KiB
Markdown
29 lines
1.2 KiB
Markdown
---
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title: Forms of a Parabola
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---
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## Standard Form / General Form
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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`.
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Standard form (also known as General Form) of a parabola can be represented in the equation below:
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y=ax<sup>2</sup>+bx+c
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## Factored Form
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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.
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Factored form of a parabola can be represented in the equation below:
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y=a(x-m)(x-n)
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## Vertex Form
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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`.
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Vertex form of a parabola can be representes in the equation below:
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y=a(x-h)<sup>2</sup>+k
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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.
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