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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 ⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇⬇

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 symmet class=

Respuesta :

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

[tex] x=0.5 [/tex]

Formula for the function:

we know that this is graph of parabolas

so, we can use vertex formula of parabola

[tex] y=a(x-h)^2+k [/tex]

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

[tex] y=a(x-0.5)^2-0.75 [/tex]

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

[tex] -1=a(0-0.5)^2-0.75 [/tex]

[tex] -0.25=a(0-0.5)^2 [/tex]

[tex] -0.25=0.25a [/tex]

[tex] a=-1 [/tex]

now, we can plug it back

and we get

[tex] y=-1(x-0.5)^2-0.75 [/tex]

now, we can expand it

[tex] y=-x^2+x-0.25-0.75 [/tex]

[tex] y=-x^2+x-1 [/tex]

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

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