Complete question
The complete question is shown on the first uploaded image
Answer:
The function is [tex]y = \frac{1}{18} (x -4 )^2 + 3.5[/tex]
The domain is [1, 7]
Step-by-step explanation:
Generally from the Graph we can see that
For the y-coordinate the point of symmetry is [tex]y = g = 4[/tex]
For the x-coordinate the point of symmetry is x = 4
The general form of quadratic equation representing this type of curve is
[tex]y = b(x-g)^2 + u[/tex]
Now considering the coordinate (4, 3.5) along the axis of symmetry we have that
[tex]3.5 = b(4-4)^2 + u[/tex]
=> [tex]u = 3.5[/tex]
Now considering point B having the coordinates (7,4)
[tex]4 = b(7-4)^2 + 3.5[/tex]
[tex]4 = 9b + 3.5[/tex]
[tex]b = \frac{1}{18}[/tex]
Generally the function that define the given graph is
[tex]y = \frac{1}{18} (x -4 )^2 + 3.5[/tex]
From the graph the first element for x is 1 (i.e [1 . 4] )and the last element for x is 7 (i.e [7,4])
So the domain of the function is [1, 7]
