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1、y=a(x-h)2+k的图像和性质Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.学习目标1、会用描点法画出二次函数y=a(x-h)²+k的图像2、了解抛物线y=a(x-h)²+k的开口方向、顶点坐标、对称轴、最值。3、掌握把抛物线y=ax²平移至y=a(x-h)²+k的规律Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5Cl
2、ientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.复习提问：1.我们已学过二次函数的哪几种特殊形式的图像和性质？y=ax2y=ax2+ky=a(x-h)22.回忆它们的性质。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.抛物线开口方向对称轴顶点最值增减情况y=ax²a>0,向上X=0(0,0)当x=0时,y有最小值0x<0时
3、,y随x的增大而减小;x>0时,y随x的增大而增大a<0,向下X=0(0,0)当x=0时,y有最大值0x<0时,y随x的增大而增大;x>0时,y随x的增大而减小.y=ax²+ka>0,向上X=0(0,k)当x=0时,y有最小值cx<0时,y随x的增大而减小;x>0时,y随x的增大而增大a<0,向下X=0(0,k)当x=0时,y有最大值cx<0时,y随x的增大而增大;x>0时,y随x的增大而减小.y=a(x-h)²a>0,向上X=h(h,0)当x=h时,y有最小值0x<0时,y随x的增大而减小;x>0时,y随x的增大而增大a<0
4、,向下X=h(h,0)当x=h时,y有最大值0xh时,y随x的增大而减小.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.1.填表抛物线开口方向对称轴顶点坐标(0,0)(1,0)(-1,0)(0,0)(0,1)(0,-1)向下向下向下向上向上向上x=0x=0x=0x=0x=1x=-1Evaluationonly.CreatedwithAspos
5、e.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Oxy1234512345–5–4–3–2–1–5–4–3–2–1（0,3）（0,-3）如何由的图象得到的图象。2.上下平移、3312--=xy3312+-=xyEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Oxy1234512345–
6、5–4–3–2–1–5–4–3–2–1x=-2(-2,0)(2,0)x=2如何由的图象得到的图象。、3.左右平移Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.y=ax2y=a(x-h)2y=ax2+ky=ax2k>0k<0上移下移h>0右移h<0左移说出平移方式，并指出其顶点与对称轴。上加下减左加右减Evaluationonly.CreatedwithAspose.Slid
7、esfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.1.画出函数的图像.指出它的开口方向、顶点与对称轴、x…-4-3-2-1012………解:先列表再描点后连线.-5.5-3-1.5-1-1.5-3-5.5合作探究：Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.12345x-1-2-3-4-5-6-7
8、-8-91yo-1-2-3-4-5-10直线x=－1描点、连线讨论抛物线的开口向下,对称轴是直线x=－1,顶点是(－1,－1).抛物线的开口方向、对称轴、顶点、最值?X=-1时，y最大值=-1Evaluationonly.CreatedwithAspose.Slidesfor
