Answer:
[tex]\textsf{B)} \quad y=3x^2-6x-3[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is the leading coefficient.\\\end{minipage}}[/tex]
If the vertex is (1, -6) then h = 1 and k = -6:
[tex]\implies y=a(x-1)^2+(-6)[/tex]
[tex]\implies y=a(x-1)^2-6[/tex]
From inspection of the answer options, the leading coefficient is 3.
Therefore, a = 3:
[tex]\implies y=3(x-1)^2-6[/tex]
Expand the equation to standard form:
[tex]\implies y=3(x^2-2x+1)-6[/tex]
[tex]\implies y=3x^2-6x+3-6[/tex]
[tex]\implies y=3x^2-6x-3[/tex]
