Answer:
range (- ∞, 2 ]
Explanation:
the range of the quadratic function is the valid values of y that the function covers.
given a quadratic in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
x = -

g(x) = - x² - 10x - 23
with a = - 1, b = - 10 , then
x = -
= - 5
substitute x = - 5 into g(x)
g(- 5) = - (- 5)² - 10(- 5) - 23
= - 25 + 50 - 23
= 25 - 23
= 2
since the coefficient of the x²- term < 0 then maximum value of 2
range is (- ∞ , 2 ]