Question

50 POINTS + WILL MARK AS THE BRAINLIEST

Answer 1

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

$x=0.5$

Formula for the function:

we know that this is graph of parabolas

so, we can use vertex formula of parabola

$y=a(x-h)^2+k$

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

$y=a(x-0.5)^2-0.75$

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

$-1=a(0-0.5)^2-0.75$

$-0.25=a(0-0.5)^2$

$-0.25=0.25a$

$a=-1$

now, we can plug it back

and we get

$y=-1(x-0.5)^2-0.75$

now, we can expand it

$y=-x^2+x-0.25-0.75$

$y=-x^2+x-1$

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

Answer 2

Answer is option D...........