Answer:
The correct option is A.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex] ..... (1)
Where, (h,k) is vertex and a is a constant.
From the given graph it is clear that the vertex of the graph is (3,-7) and y-intercept is (0,2).
Substitute h=3 and k=-7 in equation (1).
[tex]y=a(x-3)^2-7[/tex]
The y-intercept is (0,2). So, substitute c=0 and y=2 in the above equation to find the value of a.
[tex]2=a(0-3)^2-7[/tex]
[tex]2+7=a(3)^2[/tex]
[tex]9=9a[/tex]
Divide both sides by 9.
[tex]1=a[/tex]
The value of a is 1.
Substitute a=1, h=3 and k=-7 in equation (1).
[tex]y=1(x-3)^2-7[/tex]
[tex]y=x^2-6x+9-7[/tex]
[tex]y=x^2-6x+2[/tex]
The equation of the parabola is [tex]y=x^2-6x+2[/tex].
Therefore the correct option is A.
