1. PARABOLAS GOAL: GRAPH AND EQUATIONS OF PARABOLAS

2. DEFINITIONS Focus – lies on the axis of symmetry Vertex – lies halfway between the focus and the directrix Directrix – perpendicular to the axis of symmetry Parabola – the graph of a quadratic equation (u-shaped)

3. STANDARD EQUATION OF A PARABOLA WITH VERTEX AT (0,0) Equation - X 2 = 4py Y 2 = 4px Focus – (0,p) (p,0) Directrix - Y = -p X = -p Axis of Symmetry – Vertical (X=0) Horizontal (y=0)

4. EXAMPLE 1 Identify the focus and the directrix of the parabola given by X=3/4y 2. Draw the parabola.

5. EXAMPLE 2 Write an equation of the parabola shown below

6. PARABOLAS IN THE REAL WORLD You will find five pictures on the internet that displays a parabola and print them out. We will use them for discussing and graphing.