Course Activity Equation of a Parabola Based on Its Focus and Directrix The Lesson Activities will help you meet these educational goals: ∙ Content Knowledge—You will derive the equation of a parabola given a focus and directrix. ∙ Mathematical Practices—You will make sense of problems and solve them. Directions Pleasesave this documentbefore you begin working on the assignment. Type your answers directly in the document. ________________________________________________________________________ _ Teacher-Graded Activities Write a response for each of the following activities. Check the Evaluation section at the end of this document to make sure you have met the expected criteria for the assignment. When you have finished, submit your work to your teacher. 1. Deriving the Equation of a Parabola Given a Focus and Directrix1 ( ) y x h k = − + 4 p a. The vertex form of the equation of a verticalparabolais given bywhere (h,k) is the vertex of the parabola and the absolute value ofpis the distance from the vertex to the focus, which is also the distance from the vertex to the directrix. You will use the GeoGebra geometry tool to create a vertical parabola and write thevertex form of its equation. OpenGeoGebra, and complete each step below. If youneed help, follow theseinstructionsfor using GeoGebra. i. Mark the focus of the parabola you are going to create atF(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?2 ,
