Answer:
The correct option is C.
Step-by-step explanation:
The function has axis of symmetry at [tex]x=6[/tex], it represents that the parabola is along the x-axis and the standard form of parabola is
[tex]y=a(x-h)^2+k[/tex]
Where, a is scale factor and (h,k) is vertex.
The maximum or minimum value of a quadratic function is the vertex of parabola. So, vertex of parabola is (6,4).
[tex]y=a(x-6)^2+4[/tex]
The y-intercept of the function is (0,-32)
[tex]-32=a(0-6)^2+4[/tex]
[tex]-32-4=36a[/tex]
[tex]-36=36a[/tex]
[tex]a=-1[/tex]
Therefore required equation of parabola is
[tex]y=-(x-6)^2+4[/tex]
[tex]y=-(x^2-12x+36)+4[/tex]
[tex]y=-x^2+12x-36+4[/tex]
[tex]y=-x^2+12x-32[/tex]
Therefore option C is correct.
