# Parabola Shifts (Horizontal Parabola)

Author:
Annie
Topic:
Parabola

## Directions

1. Use the sliders to explore the parameters involved in determining the equation of the parameters. 2. Answer the questions below.

## Question 1

How is this parabola different from the one you explored in the last section? Is this relation a function?

## Question 2

If you have not already played with the directrix slider, do so now! How does changing the slope effect the relation?

## Match My Equations

﻿﻿﻿﻿﻿Click on the Match My Equation checkboxes and move the focus and directrix to match up the equations. You will notice that the equations are not written in the form. Work with your partner to rewrite the equations so that you are convinced they are equivalent.

## Forms of Equations

You are already familiar with writing a quadratic function in the form . The conics form is The conics form of the parabola equation (the one you'll find in advanced or older texts) is: (credit to purplemath.com)
regular: 4p(y – k) = (x – h)2  sideways: 4p(x – h) = (y – k)2
where p is the distance between the focus and the vertex. There are more complicated forms of the equation when the directrix is not horizontal or vertical that involve xy terms in the equation.

## Use for questions 3 - 5

A parabola open horizontally and has a focus at (5,2) and a vertex at (3,2).

## Question 3

What is the directrix of the parabola?

## Question 4

What is the equation of the parabola?

## Question 5

Find another point on this parabola. Then verify that it meets the requirement of being equidistant from both the focus and the directrix.