Parabola PowerPoint  Debra Schablik Western Governor’s University

Lesson 10.2 Parabolas  Goal: Graph and write equations of parabolas

Creation of a Parabola  A conic section is a curve formed by the intersection of a plane a double-napped cone (Zoebel, )

Definition of a Parabola (Larson, Boswell, Kanold & Stiff, 2005)

Where are parabolas? (Internet Access is Required) They’re everywhere. Put arrow on icon and click. Click power point icon on task bar to continue with slide show after video is finished. (Part 1-They’re Out There!!!, 2008)

Parabolas  Parabolas with vertex at (0,0) and open up or down are in the form:

4py  If positive, the parabola opens up  If negative, the parabola opens down

Parabolas with vertex at (0,0) and open right or left are in the form:

4px  If positive, the parabola opens to the right  If negative, the parabola opens to the left

The Axis of Symmetry  For parabolas that open up or down, the axis of symmetry is the line x = the x- coordinate of the vertex.  For parabolas that open right or left, the axis of symmetry is the line y = the y- coordinate of the vertex.

The Focus  The focus is an ordered pair (x,y), and is INSIDE the parabola and on the axis of symmetry.

The Directrix  The directrix is a line that is perpendicular to the axis of symmetry and is always OUTSIDE the parabola.

4p  4p is the number in front of the variable that has a coefficient of 1.  is the distance from the vertex to the focus and/or the distance from the vertex to the directrix.

The Vertex  The vertex lies halfway between the focus ( x, y) and the directrix (line).

Focal Chord  The focal chord, 2p, is measured from the focus and gives the true width of the parabola.

#32 Identify the focus and directrix of the parabola.

opens up, with vertex at origin, to get the focus, plot the point 2 units inside the parabola and on the axis of symmetry, thus the focus is.

The directrix is perpendicular to the axis of symmetry and is also 2 units away from the vertex, so the equation of the directrix is

#34 Identify the focus and directrix of the parabola.

opens left, with the vertex at origin. To find the focus, plot the point 4 units inside the parabola and on the axis of symmetry, thus the focus is.

The directrix is perpendicular to the axis of symmetry and is also 4 units away from the vertex, so the equation of the directrix is

From the graph, the vertex is at the origin, (0,0), and the directrix is 2 units away from the vertex. The parabola opens up, so the equation is in form. Since p = 2, the equation is Example #2 Writing the equation of a parabola (Larson, Boswell, Kanold & Stiff, 2005)

#10 Write the standard form of the equation of the parabola with the given focus or directrix with the vertex at (0,0). Focus Since the focus has to be inside the parabola and lie on the axis of symmetry, this parabola opens up, and is the form The distance p is the distance from the vertex to the focus, or in this case 3. So the equation is

References  Zoebel, Edward A. ( ) Retrieved April 13, Welcome to Zona Land bolaPic1.jpg  Larson, Ron, Laurie Boswel, Timothy Kanold and Lee Stif. (2005). Algebra 2. Evanston Illinois: McDougall Little.  They’re Out There! (n.d.) retrieved April 20, 2008 from