Math methods units 1&2 help

[Rose34]

 A family of parabolas satisfies the rule y = ax^2 + 2x + a.
Express ax^2 + 2x + a in the form a(x + b)^2 + c for real numbers b and c.

Could someone please help me, I am stuck and have no idea how to start.

Thanks in advance!

[sara.vce]

A family of parabolas satisfies the rule y = ax^2 + 2x + a.
Express ax^2 + 2x + a in the form a(x + b)^2 + c for real numbers b and c.

Here's what you could do. Hope it makes sense!

Complete the square for ax^2+2x+a
either use the formula:
= take out a as a common factor
= add 1/2*(2/a)^2 then subtract 1/2*(2/a)^2
= factorise into turning point form
or
use CAS:
menu>3>5: complete the square
completesquare(a x x^2 + 2 x x + a=0,x)
-> a(x+1/a)^2 + (a^2-1)/a