Question

Please look at the photo. Thank you.

Answer 1

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 = -
`(b)/(2a)`

g(x) = - x² - 10x - 23

with a = - 1, b = - 10 , then

x = -
`(-10)/(-2)` = - 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 ]