Answer: The correct option is (A). [tex]y=-(x+5)^2+4.[/tex]
Step-by-step explanation: Given that the co-ordinates of the vertex of a parabola is (-5, 4).
We are to select the correct option that could be the equation of the given parabola.
We know that the standard equation of a [parabola with vertex (h, k) is given by
[tex]y=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~(i)[/tex]
Taking a = -1, equation (i) becomes
[tex]y=-(x-h)^2+k.[/tex]
If the vertex is (h, k) = (-5, 4), then the equation of the parabola becomes
[tex]y=-\{x-(-5)\}^2+4\\\\\Rightarrow y=-(x+5)^2+4.[/tex]
Therefore, if we take a = - 1, then [tex]y=-(x+5)^2+4.[/tex] could be the equation of the parabola.
Thus, (A) is the correct option.
