Question

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

Answer 1

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)

$h=\dfrac{0+2}{2}=\dfrac{2}{2}=1\\\\k=g(h)\to k=g(1)=-6(1-2)(1)=-6(-1)(1)=6$

Vertex: (1, 6).

Answer 2

The function, when graphed, looks like this: