[size=150]The parabola below is shown in FACTORED FORM [math]y=a\left(x-\alpha\right)\left(x-\beta\right)[/math] where [math]\alpha[/math] and [math]\beta[/math] are the ROOTS (or the zeros) of the equation.[br][br]In this task you will explore the link between the values of the roots and the equation of the axis of symmetry.[br][br][/size][b]Note:[/b] root1 should always to the right of root2 for the colours to match!

[size=150][b]Question 1:[/b][br][list][*]Set [math]a=1[/math][/*][*]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?[/*][/list][/size]

[size=150][b]Question 2:[/b][br][list][*]Set [math]a=1[/math][/*][*]Set root 2 = 0[/*][*]Set root1 = 3[/*][*]Write down the roots and the equation of the axis of symmetry[/*][/list][/size]

[size=150][b]Question 3:[/b][br][list][*]Set [math]a=1[/math][/*][*]Set root 2 = -4[/*][*]Set root1 = 0[/*][*]Write down the roots and the equation of the axis of symmetry[/*][/list][b]Based on the three examples you have looked at so far, describe the relationship between the roots and the axis of symmetry.[/b][br][/size]

[size=150][b]Question 4:[/b][list][*]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.[/*][/list][/size]