Q1 The quadratic function $f ( x ) = 2 x ^ { 2 } + a x - 1$ in $x$ satisfies $$f ( - 1 ) \geqq - 3 , \quad f ( 2 ) \geqq 3 .$$ Let us consider the minimum value $m$ of $f ( x )$. (1) $m$ can be expressed in terms of $a$ as $$m = - \frac { \mathbf { A } } { \mathbf{B} } a ^ { 2 } - \mathbf { C }$$ (2) The range of the values of $a$ such that $f ( x )$ satisfies condition (1) is $$\mathbf { D E } \leqq a \leqq \mathbf { F } .$$ (3) The value of $m$ is maximized when the axis of symmetry of the graph of $y = f ( x )$ is the straight line $x = \mathbf { G }$, and then the value of $m$ is $\mathbf { H I }$. (4) The value of $m$ is minimized when the axis of symmetry of the graph of $y = f ( x )$ is the straight line $x = \mathbf { J K }$, and then the value of $m$ is $\mathbf { L M }$.
Q1 The quadratic function $f ( x ) = 2 x ^ { 2 } + a x - 1$ in $x$ satisfies
$$f ( - 1 ) \geqq - 3 , \quad f ( 2 ) \geqq 3 .$$
Let us consider the minimum value $m$ of $f ( x )$.\\
(1) $m$ can be expressed in terms of $a$ as
$$m = - \frac { \mathbf { A } } { \mathbf{B} } a ^ { 2 } - \mathbf { C }$$
(2) The range of the values of $a$ such that $f ( x )$ satisfies condition (1) is
$$\mathbf { D E } \leqq a \leqq \mathbf { F } .$$
(3) The value of $m$ is maximized when the axis of symmetry of the graph of $y = f ( x )$ is the straight line $x = \mathbf { G }$, and then the value of $m$ is $\mathbf { H I }$.\\
(4) The value of $m$ is minimized when the axis of symmetry of the graph of $y = f ( x )$ is the straight line $x = \mathbf { J K }$, and then the value of $m$ is $\mathbf { L M }$.