It's the quadratic function. The graph is a parabola.
[tex]g(x)=-6(x-2)(x)[/tex]
x-intercepts:
[tex]g(x)=0\to-6(x-2)(x)=0\iff x-2=0\ \vee\ x=0\\\\x=2\ \vee\ x=0[/tex]
y-intercept:
[tex]g(0)=-6(0-2)(0)=0[/tex]
The vertex (h, k)
[tex]h=\dfrac{0+2}{2}=\dfrac{2}{2}=1\\\\k=g(h)\to k=g(1)=-6(1-2)(1)=-6(-1)(1)=6[/tex]
Vertex: (1, 6).
