Consider the two quadratic functions $$f ( x ) = - 2 x ^ { 2 } , \quad g ( x ) = x ^ { 2 } + a x + b$$ Function $g ( x )$ satisfies the following two conditions: (i) the value of $g ( x )$ is minimized at $x = 3$; (ii) $g ( 4 ) = f ( 4 )$. (1) From condition (i) we see that $a = -$ A . Further, from condition (ii) we see that $b = - \mathbf { B C }$. Hence the minimum value of function $g ( x )$ is $- \mathbf { D E }$. (2) Let us find the value of $x$ such that $f ( x ) = g ( x )$ and $x$ is not 4 . Since $x$ satisfies $$x ^ { 2 } - \mathbf { F } x - \mathbf { G } \mathbf { G } = 0 \text {, }$$ we obtain $x = - \mathbf { H }$. (3) The value of $f ( x ) - g ( x )$ on $- \mathrm { H } \leqq x \leqq 4$ is maximized at $x = \square$, and its maximum value is JK.
Consider the two quadratic functions
$$f ( x ) = - 2 x ^ { 2 } , \quad g ( x ) = x ^ { 2 } + a x + b$$
Function $g ( x )$ satisfies the following two conditions:\\
(i) the value of $g ( x )$ is minimized at $x = 3$;\\
(ii) $g ( 4 ) = f ( 4 )$.\\
(1) From condition (i) we see that $a = -$ A . Further, from condition (ii) we see that $b = - \mathbf { B C }$. Hence the minimum value of function $g ( x )$ is $- \mathbf { D E }$.\\
(2) Let us find the value of $x$ such that $f ( x ) = g ( x )$ and $x$ is not 4 . Since $x$ satisfies
$$x ^ { 2 } - \mathbf { F } x - \mathbf { G } \mathbf { G } = 0 \text {, }$$
we obtain $x = - \mathbf { H }$.\\
(3) The value of $f ( x ) - g ( x )$ on $- \mathrm { H } \leqq x \leqq 4$ is maximized at $x = \square$, and its maximum value is JK.