Answer:
The correct option is C) [tex]x=-(y+12)^2+5[/tex].
Step-by-step explanation:
Consider the provided information.
The equation of a parabola (horizontal) is:
[tex]x=a(y-k)^2+h[/tex]
Where (h,k) are the vertex of the parabola.
Parabola opens left if the value of a is negative.
It is given that the vertex of the parabola is (5,-12) and it opens to the left.
Substitute the value of a = -1, h = 5 and k = -12 in the equation of parabola.
[tex]x=-1(y-(-12))^2+5[/tex]
[tex]x=-(y+12)^2+5[/tex]
For better understanding refer to the figure 1:
Therefore, the correct option is C) [tex]x=-(y+12)^2+5[/tex].
