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12 Cards in this Set
- Front
- Back
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The equation of a parabola is:
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y = ax² + bx + c or y = a(x - h)² + k
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What is the definition of a parabola?
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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).
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Define the axis of symmetry:
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the line perpendicular to the directrix and containing the focus.
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Define the vertex:
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the point on the axis of symmetry that is equidistant from the focus and directrix.
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What are the coordinates for the focus?
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(h, k + p)
where p = focal length |
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What is the formula for the directrix?
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y = k - p
where p > 0 |
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Define focal length:
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the directed distance from the vertex to the focus.
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What is the formula for a parabola?
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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. |
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For any parabola, do a & p have to have the same sign?
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yes, if they are pos. the parabola opens up;
if negative, the parabola opens down. |
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If the focus is above the vertex, then:
If the focus is below the vertex, then: |
p > 0
p < 0 |
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a =
p = |
a = 1/4(p)
p = 1/4(a) |
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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. |
