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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.