Parabola Shifts (Vertical Parabola)
Move point P around the parabola. What do you notice about the relationship between the point P (a point on the parabola) and the Focus and Directrix. Note: The Focus is a given point and the Directrix is a given line. Together they define the parabola.
What happens as you move the focus and directrix closer together? Farther apart?
Match My Equations
Forms of Equations
- 4p(y – k) = (x – h)2
Use the 2 forms of writing the equation of a parabola (above) to determine the value of a (in terms of p - the distance of the vertex from the focus.) Use the "regular" form.
Given the Focus (0,4) and the Directrix y = -2, what is the equation of the parabola? (Hint: Find the vertex first.)
Use for Questions 5 - 7
Question 5 (See information above.)
What is the equation of the parabolic arch? (Center the arch on the y-axis and let the x-axis represent the ground/base.)
Question 6 (See information above.)
What are the focus and directrix of the arch?
Question 7 (See information above.)
What is the equation of the parabolic arch in "conics form"?
Given a parabola with a a focus of (2,5) and a directrix of y = -1, find the equation of the parabola.
Question 9 - BONUS
Given a parabola that contains the points (-1, 5) and (3, 8) and has the directrix y = -2, find the focus of the parabola. (Hint: Make your own Geogebra sheet to find the intersection of the equations you use to find the focus!)