Question

The vertex of the parabola below is at the point (-4,-2) wich of the equations below could be the one for this parabola

Answer 1

X= -2(y+2)^2-4

Explanation:

Answer 2

The parabola with with a vertex at (-4,-2) represents any member of parabolas with the equation
`y(x)=a(x+4)^2-2` where
`a` is any real number with the exception that
`a\\eq 0`.

The reason any equation of the form
`y(x)=a(x+4)^2-2` 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
`y=x^2`. The different variations are archived by varying the constant
`a`. When
`a` is negative, the parabolas will face downwards. When
`a` is negative, the parabolas will be face downwards.