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12 Cards in this Set

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The equation of a parabola is:
y = ax² + bx + c or y = a(x - h)² + k
What is the definition of a parabola?
A parabola is the set of all points in the plane that are equidistant from a fixed line (the directrix) and a fixed point not on the line ( the focus).
Define the axis of symmetry:
the line perpendicular to the directrix and containing the focus.
Define the vertex:
the point on the axis of symmetry that is equidistant from the focus and directrix.
What are the coordinates for the focus?
(h, k + p)
where p = focal length
What is the formula for the directrix?
y = k - p
where p > 0
Define focal length:
the directed distance from the vertex to the focus.
What is the formula for a parabola?
The equation of a parabola
with focus (h, k + p) and directrix y = k - p is:
y = a( x - h )² + k,
where a = 1/(4p) and (h,k) is the vertex.
For any parabola, do a & p have to have the same sign?
yes, if they are pos. the parabola opens up;
if negative, the parabola opens down.
If the focus is above the vertex, then:
If the focus is below the vertex, then:
p > 0
p < 0
a =
p =
a = 1/4(p)
p = 1/4(a)
How can you find the vertex of the parabola when the equation is in standard form:
ax² + bx + c, without first converting it to vertex form: a(x - h)² + k ?
1) Find the x-coordinate (h) of the
vertex by using the formula: -b/2a
2) Find the y-coordinate (K) by plugging
in this value of x and solving for y.