PARABOLAS

GOAL: GRAPH AND EQUATIONS OF PARABOLAS

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)

STANDARD EQUATION OF A PARABOLA WITH VERTEX AT (0,0)

• Equation - X2 = 4py Y2 = 4px• Focus – (0,p) (p,0)• Directrix - Y = -p X = -p• Axis of • Symmetry – Vertical (X=0) Horizontal (y=0)

EXAMPLE 1

• Identify the focus and the directrix of the parabola given by X=3/4y2. Draw the parabola.

EXAMPLE 2

• Write an equation of the parabola shown below

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.