Question

For the function f(x) = -2(x + 3)2 -1, identify the vertex, domain, and range.

Answer 1

y=a(x-h)²+k
vertex is (h,k)
the vertex is the max or minimum value of the range (y values)

when a is positive, the graph opens up and the vertex is a minimum
when a is negative, the graph opens down and the vertex is a max


domain is all possible values you can use for x



f(x) = -2(x + 3)²-1
or
f(x) = -2(x-(-3))²+(-1)

a is negative
means y=-1 is max y value, so all values from y=-1 to below is in range
vertex is (-3,-1)
(x,y)
max y value is -1
the domain is all real numbers


so

vertex: (-3,-1)
domain: all real numbers
range: -1 to -∞ (in interval notation (-∞,-1] )

Answer 2

I think this attachment will help you