what are the equations for parabola?

Question

kelangan lang sa school... takot ko kay ma'am bataller eh

Answer 1

Parabola with vertical symmetry:
y = a(x - h)² + k
vertex: (h, k)
axis of symmetry: x = h
The parabola opens upward when a > 0, downward when a < 0.

Parabola with horizontal symmetry:
x = a(y - k)² + h
vertex: (h, k)
axis of symmetry: y = k
The parabola opens to the right when a > 0, to the left when a < 0.

Answer 2

y=x^2

Answer 3

Equations

(with vertex (h, k) and distance p between vertex and focus - note that if the vertex is below the focus, or equivalently above the directrix, p is positive, otherwise p is negative; similarly with horizontal axis of symmetry p is positive if vertex is to the left of the focus, or equivalently to the right of the directrix)
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Cartesian
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Vertical axis of symmetry

(x - h)^2 = 4p(y - k) \,

y = a(x-h)^2 + k \,

y = ax^2 + bx + c \,

\mbox{where }a = \frac{1}{4p}; \ \ b = \frac{-h}{2p}; \ \ c = \frac{h^2}{4p} + k; \ \
h = \frac{-b}{2a}; \ \ k = \frac{4ac - b^2}{4a}.

x(t) = 2pt + h; \ \ y(t) = pt^2 + k \,

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Horizontal axis of symmetry

(y - k)^2 = 4p(x - h) \,

x = a(y - k)^2 + h \,

x = ay^2 + by + c \,

\mbox{where }a = \frac{1}{4p}; \ \ b = \frac{-k}{2p}; \ \ c = \frac{k^2}{4p} + h; \ \
h = \frac{4ac - b^2}{4a}; \ \ k = \frac{-b}{2a}.

x(t) = pt^2 + h; \ \ y(t) = 2pt + k \,

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Semi-latus rectum and polar coordinates

In polar coordinates, a parabola with the focus at the origin and the top on the negative x-axis, is given by the equation

r (1 - \cos \theta) = l \,

where l is the semi-latus rectum: the distance from the focus to the parabola itself, measured along a line perpendicular to the axis. Note that this is twice the distance from the focus to the apex of the parabola or the perpendicular distance from the focus to the latus rectum.

Answer 4

The equation is y^2=4*a*x.

Answer 5

a quadratic formula given it is concave up or concave down this is how to get the equations.

y = a(x-h)^2 + k
where point (h,k) is the vertex h is the number of units from the y axis and k is the number of units from the x axis

Answer 6

You can get everything about Parabola in the following link

http://en.wikipedia.org/wiki/Parabola

Answer 7

y=x sq n d vice versa