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Well, honey, the vertex of a parabola is in the form (h, k), not (h-k). So, the correct vertex form should be (-4, -2). Now, any equation that has a vertex at (-4, -2) could be the one for this parabola. Just plug that vertex into the standard form of a parabola equation and you'll have your answer.
To find the equation of a parabola given its vertex and a point on the curve, we can use the vertex form of a parabolic equation: y = a(x-h)^2 + k, where (h, k) is the vertex. Substituting the given vertex (-4, -2) into the equation gives y = a(x+4)^2 - 2. To determine the value of 'a', we also need a point that lies on the parabola. Without this additional information, there are infinitely many parabolas that could pass through the vertex (-4, -2).
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There are infinitely many such parabolas, four possibilities are: y = x² - 3 y = 5 - x² x = y² - 3 x = -1 - y² Given the focus as well would give an exact equation