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. Writing linear equation in parabolic form
GOAL: Turn general form
Standard form

4. Writing linear equation in parabolic form
Start with
Group the two x-terms
Pull out the constant with x2 from the grouping
Complete the square of the grouping
**Look back to Topic 6.3 for help**
Write the squared term as subtraction so that you end with standard form

5. Group x-terms
Pull out GCF
Complete the Square
**Remember that whatever you add in the grouping must be subtracted from the c-value**
Factor and simplify

6. Summary of Parabolas in Standard Form
Equation
Axis of symmetry
x = h
y = k
Vertex
(h, k)
Focus
Directrix
Direction of opening
Up: a>0, Down: a<0
Right: a>0, Left: a<0
Latus Rectum

7. Graph of prior example

8. You Try!!
Write the following equation in parabolic form. Then identify all of the parts.
Vertex:
(5, -32)
Focus:
(5.25, -32)
Axis of Symmetry:
Latus Rectum: 1
X=5
Direction of Opening:
Right
Directrix:
x= 4.75