1. Parabolas
Objective:
Be able to identify the vertex, focus and directrix of a parabola and create an equation for a parabola.
Thinking Skill: Explicitly assess information
and draw conclusions
Warm Up: Please pick up the three sheets on the podium & complete the half sheet warm-up.

2. Parabola
Definition: All the points (x, y) equidistant from a fixed line (directrix) and a fixed point (focus)
Standard form
Vertical – Horizontal
Directrix: y = k – p Directrix: x = h – p
Where the vertex is (h, k) and p is the directed distance to the focus.

3. Parabola Examples
Find the equation of the parabola with a vertex of (5, 2) and a focus of (3, 2)
Standard Form:
General Form:

4. Parabola Examples
Find the equation of the parabola with a focus of (-2, 3) and a directrix of y = 7
Standard Form:
General Form:

5. Parabola Examples
Find the focus, vertex & directrix of the parabola x = 0.125y y and graph the parabola.

6. Reflective Property
The tangent line to a parabola at a point P makes equal angles with the following two lines
The line passing through P and the focus
The axis of the parabola P

7. Find the equation of the tangent line to the parabola given y = x2 at the point (1,1)

8. Closing Problem
Find the vertex, focus and directrix of y = ¼ (x2 – 2x + 5)
Vertex ( 1, 1)
Focus (1, 2)
Directrix y = 0