**Problem : **
Given the following quadratic function
*f* (*x*) = 3*x*
^{2} - 12*x* + 13
, decide
whether the graph opens upward or downward, find the vertex and axis of
the graph, and find any real roots of the
function.

**Problem : **
Given the following quadratic function
*f* (*x*) = - 3*x*
^{2} - 6*x* - 3
, decide whether
the graph opens upward or downward, find the vertex and axis of the graph, and
find any real roots of the function.

**Problem : **
Given the following quadratic function
*f* (*x*) = *x*
^{2} - 8*x* + 19
, decide whether
the graph opens upward or downward, find the vertex and axis of the graph, and
find any real roots of the function.

**Problem : **
Given the following quadratic function
*f* (*x*) = *x*
^{2}
, decide whether the graph
opens upward or downward, find the vertex and axis of the graph, and find any
real roots of the function.

**Problem : **
Given the following quadratic function
*f* (*x*) = *x*
^{2} - 2*x*
, decide whether the
graph opens upward or downward, find the vertex and axis of the graph, and find
any real roots of the function.