ParabolasObjective: •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.

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.

24 ( )p x h y k 21

( )4

y x h kp

24 ( )p y k x h 21

( )4

x y k hp

Parabola Examples

• Find the equation of the parabola with a vertex of (5, 2) and a focus of (3, 2)

Standard Form:General Form:

Parabola Examples

• Find the equation of the parabola with a focus of (-2, 3) and a directrix of y = 7

Standard Form:General Form:

Parabola Examples

• Find the focus, vertex & directrix of the parabola x = 0.125y2 + 0.25y + 0.125 and graph the parabola.

Reflective PropertyThe tangent line to a parabola at a point P makes

equal angles with the following two lines

1. The line passing through P and the focus

2. The axis of the parabola

P

Find the equation of the tangent line to the parabola given y = x2 at

the point (1,1)

Closing Problem

• Find the vertex, focus and directrix of y = ¼ (x2 – 2x + 5)

• Vertex ( 1, 1)

• Focus (1, 2)

• Directrix y = 0