Answer:
To find the vertex of the quadratic function y = -2x² - 4x - 5, we can use the formula:
x = -b/2a
where a = -2 and b = -4 are the coefficients of the quadratic term and the linear term, respectively.
x = -(-4)/(2*(-2)) = -(-4)/(-4) = 1
To find the y-coordinate of the vertex, we substitute x = 1 in the function:
y = -2(1)² - 4(1) - 5 = -2 - 4 - 5 = -11
Therefore, the vertex of the quadratic function is (1, -11).