1. Advanced Geometry Conic Sections Lesson 3
Parabolas

2. Axis of Symmetry
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 F p V p
Directrix

3. Equation of a Parabola Vertex Focus Axis of Symmetry Directrix
Horizontal Axis Vertical Axis
of Symmetry of Symmetry
Equation of a Parabola
Vertex
Focus
Axis of Symmetry
Directrix
Direction of Opening

4. Example:
For the equation of each parabola, find the coordinates
of the vertex and focus, the equations of the directrix
and axis of symmetry. Then graph the equation.

5. Example:
For the equation of each parabola, find the coordinates
of the vertex and focus, the equations of the directrix
and axis of symmetry. Then graph the equation.

6. Example:
Using the graph below, write the equation for the parabola.

7. Example:
Using the graph below, write the equation for the parabola.

8. The vertex is (-4, 5), the parabola opens to the left,
Example:
Write the equation of the parabola that meets each set of conditions.
The vertex is (-4, 5), the parabola opens to the left,
and the focus is 5 units from the vertex.

9. The parabola has a focus of and a minimum point at (-1, -1).
Example:
Write the equation of the parabola that meets each set of conditions.
The parabola has a focus of
and a minimum point at (-1, -1).

10. Example:
Solve for x.