Answer:
vertex of the function is (0.5, -1.25)
Axis of symmetry at x= 0.5
[tex]y=1(x-0.5)^2-1.25[/tex]
Step-by-step explanation:
To identify the axis of symmetry, vertex and the formula for the function
we use the given graph
The minimum point on the graph is (0.5, -1.25)
The minimum point is our vertex
So vertex of the function is (0.5, -1.25)
The axis of symmetry lies at the x - coordinate of the vertex
Axis of symmetry at x= 0.5
To find the function we use vertex form
[tex]y=a(x-h)^2 +k[/tex]
[tex]y=a(x-0.5)^2-1.25[/tex]
To find out 'a' we use any point from graph . lets pick (2,1)
[tex]1=a(2-0.5)^2-1.25[/tex]
Add 1.25 on both sides
[tex]2.25=a(2-0.5)^2[/tex]
take square root on both sides
1.5 = 1.5 a
a=1
The equation becomes
[tex]y=1(x-0.5)^2-1.25[/tex]
