# Parabola Shifts (Vertical Parabola)

- Author:
- Annie

- Topic:
- Parabola

## Directions

## Question 1

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.

## Question 2

What happens as you move the focus and directrix closer together? Farther apart?

## Match My Equations

## Forms of Equations

- 4

*p*(

*y*–

*k*) = (

*x*–

*h*)

^{2}

## Question 3

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.

## Question 4

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"?

## Question 8

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!)