Question

for the graph of the function below, identify the axis of symmetry, vertex and the formula for the function

Answer 1

aos: x=0.5
vertex: (0.5,-1.25)
y= (x-0.5)(x-1.5) - 1.25

Answer 2

vertex of the function is (0.5, -1.25)

Axis of symmetry at x= 0.5

`y=1(x-0.5)^2-1.25`

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

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

`y=a(x-0.5)^2-1.25`

To find out 'a' we use any point from graph . lets pick (2,1)

`1=a(2-0.5)^2-1.25`

Add 1.25 on both sides

`2.25=a(2-0.5)^2`

take square root on both sides

1.5 = 1.5 a

a=1

The equation becomes

`y=1(x-0.5)^2-1.25`