Question

Graph the function g(x)=-6(x-2)(x)

Answer 1

The function, when graphed, looks like this:

Answer 2

It's the quadratic function. The graph is a parabola.

`g(x)=-6(x-2)(x)`

x-intercepts:

`g(x)=0\to-6(x-2)(x)=0\iff x-2=0\ \vee\ x=0\\\\x=2\ \vee\ x=0`

y-intercept:

`g(0)=-6(0-2)(0)=0`

The vertex (h, k)

`h=(0+2)/(2)=(2)/(2)=1\\\\k=g(h)\to k=g(1)=-6(1-2)(1)=-6(-1)(1)=6`

Vertex: (1, 6).