50 points + will mark as the brainliest for the graph of the function below, identify the axis of symmetry, vertex and the formula for the function. a. axis of symmetry: x = 0.5; vertex: (0.5, –0.75); f(x) = –x2 – x – 1 b. axis of symmetry: x = 0.5; vertex: (0.5, –0.75); f(x) = –x2 + 2x – 1 c. axis of symmetry: x = –0.5; vertex: (–0.5, –0.75); f(x) = –x2 + x – 1 d. axis of symmetry: x = 0.5; vertex: (0.5, –0.75); f(x) = –x2 + x – 1 the graph is down ⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇

We can look at the graph

Vertex:

we know that vertex is the point where parabola changes it's shape

we can see that

vertex is at (0.5,-0.75)

Axis of symmetry:

we know that axis of symmetry of parabola is always x-value of vertex

we can see that

x-value of vertex is 0.5

so, axis of symmetry is

Formula for the function:

we know that this is graph of parabolas

so, we can use vertex formula of parabola

where

(h,k) is vertex

Here , we got

vertex as (0.5 , -0.75)

h=0.5 and k=-0.75

now, we can plug these values

now, we need to find 'a'

we can select any one point of parabola

and then we can find 'a'

We can see that one of point is (0,-1)

so, we can plug x=0 and y=-1

now, we can plug it back

and we get

now, we can expand it

so, option-D..........Answer

this is a very good question

step-by-step explanation:

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