Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
12 Cards in this Set
 Front
 Back
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 xcoordinate (h) of the
vertex by using the formula: b/2a 2) Find the ycoordinate (K) by plugging in this value of x and solving for y. 