Answer to Question #97878 in Algebra for ALexa

Question

For the graph of the function
f ( x ) = − 2 ( x + 1 ) 2 − 4
, determine each of the following and explain how you know:
Whether the graph opens upwards or downwards
The axis of symmetry of the graph
The vertex of the graph

Answer 1

The graph opens downward because the equation of parabola in vertex form

$y=a(x-h)^2+k$ has $a=-1<0$ .

Axis of symmetry is $x=h=-1$ .

Vertex of the graph is $(h,k)=(-1,-4)$ .