Let us consider the quadratic function $$f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - ( 2 a - 1 ) x + a ,$$ where $a$ is a real number. (1) The coordinates of the vertex of the graph of $y = f ( x )$ are $$\left( \mathbf { A } a - \mathbf { B } , - \mathbf { C } a ^ { 2 } + \mathbf { D } a - \mathbf { E } \right) .$$ (2) The range of $a$ such that the graph of $y = f ( x )$ and the $x$-axis intersect at two different points, A and B , is $$a < \frac { \mathbf { F } } { \mathbf{G} } \text { or } \mathbf { H } < a .$$ (3) The range of $a$ such that the $x$-coordinates of both points A and B in (2) are greater than or equal to 0 and less than or equal to 6 is $$\mathbf { I } < a \leqq \frac { \mathbf { J K } } { \mathbf { L M } } .$$
Let us consider the quadratic function
$$f ( x ) = \frac { 1 } { 4 } x ^ { 2 } - ( 2 a - 1 ) x + a ,$$
where $a$ is a real number.\\
(1) The coordinates of the vertex of the graph of $y = f ( x )$ are
$$\left( \mathbf { A } a - \mathbf { B } , - \mathbf { C } a ^ { 2 } + \mathbf { D } a - \mathbf { E } \right) .$$
(2) The range of $a$ such that the graph of $y = f ( x )$ and the $x$-axis intersect at two different points, A and B , is
$$a < \frac { \mathbf { F } } { \mathbf{G} } \text { or } \mathbf { H } < a .$$
(3) The range of $a$ such that the $x$-coordinates of both points A and B in (2) are greater than or equal to 0 and less than or equal to 6 is
$$\mathbf { I } < a \leqq \frac { \mathbf { J K } } { \mathbf { L M } } .$$