(1)y=9/7x²-7/8x+9/5
(1)y=9/7x²-7/8x+9/5
(2)y=2/3x²+2/3x-1
(3)y=4/5x²-7/3x+1
(4)y=3/4x²-3/2x-2
(5)y=-x²+5/2x-6
(6)y=-3x²+9x-5
(7)y=4x²+16x-24
(8)y=-2x²-8x+16
(9)y=5x²-12x+10
(10)y=-x²-7x+8
要求是把这些二次函数配成顶点式或者用公式法求出顶点坐标
公式法:x的坐标的求法 -b/2a y的坐标求法:4ac-b²/4a
(1)y=9/7x²-7/8x+9/5
x=-b/2a=(7/8)/(18/7)=49/144 y=(4ac-b²)/4a=(324/35-49/64)/(36/7)=133147/80640
∴顶点(49/144,133147/80640)
(2)y=2/3x²+2/3x-1
x=-(2/3)/(4/3)=-1/2 y=(-8/3-4/9)/(8/3)=-7/6
∴顶点(-1/2,-7/6)
(3)y=4/5x²-7/3x+1
x=(7/3)/(8/5)=35/24 y=(16/5-49/9)/(16/5)=-101/144
∴顶点(35/24,-101/144)
(4)y=3/4x²-3/2x-2=3/4(x²-2x)-2=3/4(x-1)²-11/4∴顶点(1,-11/4)
(5)y=-x²+5/2x-6=-(x²-5/2x)-6=-(x-5/4)²-71/16∴顶点(5/4,-71/16)
(6)y=-3x²+9x-5=-3(x²-3x)-5=-3(x-3/2)²+7/4∴顶点(3/2,7/4)
(7)y=4x²+16x-24=4(x²+4x)-24=4(x+2)²-4×2²-24=4(x+2)²-40∴顶点(-2,-40)
(8)y=-2x²-8x+16=-2(x²+4x)+16=-2(x+2)²+24∴顶点(-2,24)
(9)y=5x²-12x+10
x=12/10=6/5 y=(200-144)/20=14/5
∴顶点(6/5,14/5)
(10)y=-x²-7x+8=-(x²+7x)+8=-(x+7/2)²+81/4∴顶点(-7/2,81/4)保证对吗?