《最简二次函数的图象》概念题

二次函数几种特殊形式的图象和性质

函数形式	顶点坐标	对称轴	最值	开口、单调性
$y = a x ^ {2}$	$( 0,0 )$	$y$轴	$\left. \begin{array} {l} {a > 0 \text {时}} \\ {x = 0 \text {时,} y _ {\text {最小值}} = 0 ;} \\ {a < 0 \text {时}} \\ {x = 0 \text {时},y _ {\text {最大值}} = 0} \end{array} \right.$	$a>0$时，抛物线开口向； $x$在对称轴侧时，$y$随$x$的增大而增大； $x$在对称轴侧时，$y$随$x$的增大而减小； $a<0$时，抛物线开口向，$x$在对称轴侧时，$y$随$x$的增大而增大； $x$在对称轴侧时，$y$随$x$的增大而减小
$y = a x ^ {2} + k$	$( 0,k )$	$y$轴	$\left. \begin{array} {l} {a > 0 \text {时}} \\ {x = 0 \text {时},y _ {\text {最小值}} = k ;} \\ {a < 0 \text {时}} \\ {x = 0 \text {时},y _ {\text {最大值}} = k} \end{array} \right.$
$y = a ( x - h ) ^ {2}$	$( h,0 )$	$x=h$	$\left. \begin{array} {l} {a > 0 \text {时,}} \\ {x = h \text {时},y _ {\text {最小值}} = 0 ;} \\ {a < 0 \text {时},} \\ {x = h \text {时},y _ {\text {最大偵}} = 0} \end{array} \right.$
$y = a ( x - h ) ^ {2} + k$	$( h,k )$	$x=h$	$\left. \begin{array} {l} {a > 0 \text {时}} \\ {x = h \text {时},y _ {\text {最小值}} = k ;} \\ {a < 0 \text {时},} \\ {x = h \text {时},y _ {\text {最大值}} = k} \end{array} \right.$

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