Consider the following quadratic function.

$g(x)=3x^2-12x+5$

$($a$)$ Write the equation in the form $g(x)=a(x-h{)}^2+k.$ Then give the vertex of its graph.

Writing in the form specified: $g(x)=$

vertex: $,$

$($b$)$ Graph the function. To do this, plot five points on the graph of the function: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph$-$a$-$function button.