Final answer:
The vertex of the function y = -(x+2)(x+4) is found by locating the axis of symmetry between the roots x = -2 and x = -4, resulting in the vertex being at (-3, -1).
Step-by-step explanation:
The vertex of a quadratic function can be found by converting the function into vertex form or by using the formula x = -b/(2a) for a quadratic equation ax2 + bx + c. However, in this case, the function y = -(x+2)(x+4) is already factored, which makes finding the vertex straightforward.
To find the vertex of the parabola represented by this function, we need to find the axis of symmetry which is located exactly between the roots of the equation. The roots are x = -2 and x = -4.
The axis of symmetry is halfway between these two values, which can be calculated as x = (-2 + -4)/2 = -3. Plugging this value back into the function gives us the y-coordinate of the vertex: y = -(-3+2)(-3+4) = -1.
Therefore, the vertex of the parabola is (-3, -1).