# Axis of Symmetry - Factored Form

Topic:
Symmetry
The parabola below is shown in FACTORED FORM where and are the ROOTS (or the zeros) of the equation. In this task you will explore the link between the values of the roots and the equation of the axis of symmetry. Note: root1 should always to the right of root2 for the colours to match!
Question 1:
• Set
• Set root 2 = 0
• Set root1 = 2
• Write down the roots and the equation of the axis of symmetry
• Change the value of a; what impact does this have on the roots?
Question 2:
• Set
• Set root 2 = 0
• Set root1 = 3
• ﻿Write down the roots and the equation of the axis of symmetry
Question 3:
• Set
• Set root 2 = -4
• Set root1 = 0
• Write down the roots and the equation of the axis of symmetry
Based on the three examples you have looked at so far, describe the relationship between the roots and the axis of symmetry.
Question 4:
• Select your own values for root1 and root2
• Investigate the relationship between the equation of the axis of symmetry and the roots of the equation.
• What conclusions can you come to?
• Write a rule that allows you to find the equation of the axis of symmetry from the roots of the parabola.