10.2 Parabolas Algebra 2

Definitions Parabola: The set of all pints equidistant from a point called the focus and a line called the directrix. The focus lies on the axis of symmetry, and the directrix is perpendicular to the axis of symmetry.

Diagram of a Parabola

Standard Equation of A Parabola (Vertex at origin) The standard form of the equation of a parabola with vertex at (0, 0) is as follows… Equation Focus Directrix Axis of Symmetry

Example: Identify the focus and the directrix of the parabola given by Then draw the parabola.

Example Identify the focus and the directrix of the parabola given by Then graph the parabola.

More Examples

Example: Write the equation of the parabola shown below.

Example: Write the equation of the parabola shown below.

Additional Examples

Example: A microphone has a parabolic reflector around it to capture sound. The microphone is placed at the focus of the parabol to reflect as much sound as possible to the microphone. A cross section of the reflector is shown.

Example: (Continue) Write an equation for the cross section of the reflector How hish is the microphone above the vertex?

Example: A store uses a parabolic mirror to see all of the aisles in the store. A cross section of the mirror is shown.

Example (Continue) Write an equation for the cross section of the mirror. What is the focus of the cross section?

More Examples: