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

Answer:

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

Step-by-step 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  $a\neq 0$.

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.