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1. PARABOLAS
Topic 7.2

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
2
1.5
DIRECTRIX
FOCUS Same Distance!
POINT

3. Writing linear equation in
parabolic form
 GOAL: Turn
2
into
y ax bx c
  
2
( )
y a x h k
  

4. Writing linear equation in
parabolic form
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
2
y ax bx c
  
2
( )
y a x h k
  

5. **Remember that whatever you add in the
grouping must be subtracted from the c-value**
Group x-terms
Pull out GCF
Complete the Square
Factor and simplify
4
))
2
(
(
3 2



 x
y
or
4
)
2
(
3 2


 x
y
12
16
)
4
4
(
3 2




 x
x
y
____
16
___)
4
(
3 2




 x
x
y
16
)
4
(
3 2


 x
x
y
16
)
12
3
( 2


 x
x
y
16
12
3
: 2


 x
x
y
Example

6. Why write in parabolic form?
It gives you necessary information to draw the parabola
Equation
Axis of symmetry x = h y = k
Vertex (h, k) (h, k)
Focus
Directrix
Direction of opening Up: a>0, Down: a<0 Right: a>0, Left: a<0
Latus Rectum
2
( )
y a x h k
  
2
( )
x a y k h
  
1
,
4
h k
a
 

 
 
1
,
4
h k
a
 

 
 
1
4
y k
a
 
1
4
x h
a
 
1
units
a
1
units
a

7. Graph of prior example
2
3( ( 2)) 4
y x
   
1
3

8. You Try!!
Write the following equation in parabolic form. State
the vertex, axis of symmetry and direction of opening.
2
10 7
x y y
  
2
Parabolic form: ( 5) 32
x y
  
Vertex: (-32,5)
Axis of symmetry: y 5

Direction of Opening: right