Download PARABOLAS

PARABOLAS
Topic 7.2
Definition

The set of all points in a plane that are
the same distance from a given point
called the focus and a given line called
the directrix.
3.5
3
2.5
FOCUS
POINT
Same Distance!
2
DIRECTRIX
1.5
Writing linear equation in
parabolic form

GOAL: Turn y  ax  bx  c into
2
y  a ( x  h)  k
2
Writing linear equation in
parabolic form
y  ax 2  bx  c
1.
Start with
2.
Group the two x-terms
3.
Pull out the constant with x2 from the grouping
4.
Complete the square of the grouping
**Look back to Topic 6.3 for help**
5.
Write the squared term as subtraction so that you
end with
y  a ( x  h)  k
2
Example : y  3x  12 x  16
2
y  (3x 2  12 x)  16
y  3( x 2  4 x)  16
Group x-terms
Pull out GCF
y  3( x 2  4 x  ___)  16  ____Complete the Square
**Remember that whatever you add in the
grouping must be subtracted from the c-value**
y  3( x  4 x  4)  16  12
2
y  3( x  2) 2  4 or
y  3( x  (2)) 2  4
Factor and simplify
Why write in parabolic form?
It gives you necessary information to draw the parabola
Equation
y  a ( x  h) 2  k
x  a( y  k ) 2  h
Axis of symmetry
x=h
(h, k)
y=k
(h, k)
Vertex
Focus
1 

h
,
k



4a 

1
Directrix
yk
4a
Direction of opening Up: a>0, Down: a<0
Latus Rectum
1
units
a
1 

h

,k 

4a 

1
x  h
4a
Right: a>0, Left: a<0
1
units
a
Graph of prior example
2
y  3( x  (2))  4
1
3
You Try!!
Write the following equation in parabolic form. State
the vertex, axis of symmetry and direction of opening.
2
x  y  10 y  7
2
Parabolic form: x  ( y  5)  32
Vertex: (-32,5)
Axis of symmetry: y  5
Direction of Opening: right