#### Objectives

- Students will identify how each conic results from slicing cones.
- Students will understand the locus definition of a parabola.
- Students will describe how the values of
*a,**h*, and*k*in the vertex form of the equation of a parabola affect its graph. - Students will use the locus definition of a parabola to derive the equation of a parabola and will describe the relationships among the focus, the directrix, and the values in the vertex form of a parabola.

#### Vocabulary

- circle
- ellipse
- parabola
- hyperbola
- axis of symmetry
- focus
- directrix

#### About the Lesson

This lesson involves observing how each of the conic sections is formed and connecting the locus definition of a parabola with the vertex form of a parabola.

As a result, students will:

- Explain how each of the conic sections is formed.
- Manipulate a point on a parabola and the focus of a parabola to discover the locus definition.
- Manipulate a, h, and k in the vertex form of a parabola to observe the effects of each value.
- Use the locus definition to derive the equation of a parabola given the focus, directrix, and any point on the parabola.
- Identify the relationships among the values of the vertex form of a parabola and the focus.