Sure, let's match the given equation y=-(x+6)^(2)+4 with three possible equations.
The given equation is y=-(x+6)²+4. This is a quadratic equation. The standard form for a quadratic function is y=a(x-h)²+k where (h,k) is the vertex of the parabola.
So the vertex for the given equation is (-6,4), since the x-coordinate of the vertex is opposite of the number added to x inside the parentheses, and the y-coordinate of the vertex is the number added or subtracted outside the parentheses.
Let's compare this with the three provided equations:
1. Equation A is y=-(x + 3)²+2. The vertex here is (-3,2).
2. Equation B is y=-(x - 3)²+2. The vertex here is (3,2).
3. Equation C is y=-(x + 6)²+4. The vertex here is (-6,4).
Comparing the vertices of the given equation and the three provided equations, we see that the vertex of equation C, (-6,4), matches that of the given equation.
Therefore, the given equation y=-(x+6)^(2)+4 matches with equation C.