The parabola with with a vertex at (-4,-2) represents any member of parabolas with the equation [tex]y(x)=a(x+4)^2-2[/tex] where [tex]a[/tex] is any real number with the exception that [tex]a\neq 0[/tex].
The reason any equation of the form [tex]y(x)=a(x+4)^2-2[/tex] works is that there are an infinite number of parabolas with a vertex at (-4,-2). All of these parabolas are formed by applying some transformation that involves a vertical translation of -2 and a horizontal translation of -4 on the parabola [tex]y=x^2[/tex]. The different variations are archived by varying the constant [tex]a[/tex]. When [tex]a[/tex] is negative, the parabolas will face downwards. When [tex]a[/tex] is negative, the parabolas will be face downwards.
