用配方法求下列抛物线的顶点坐标和对称轴y=-3x²-2x+1,y=2x²+3x-1,y=-3x²+2x+3

Question

用配方法求下列抛物线的顶点坐标和对称轴
y= -3x²-2x+1 , y=2x²+3x-1 ,y= -3x²+2x+3

Answer 1

y=-3x²-2x+1
=(-3x²-2x)+1
=-3[x²+(2/3)x]+1
=-3[x²+(2/3)x+(1/3)²]+1+3×(1/3)²
=-3[x+(1/3)]²+4/3
抛物线的顶点坐标为(-1/3 ,4/3),对称轴为x=-1/3
y=2x²+3x-1
=(2x²+3x)-1
=2[x²+(3/2)x]-1
=2[x²+(3/2)x+(3/4)²]-1-2×(3/4)²
=2[x+(3/4)]²-17/8
抛物线的顶点坐标为(-3/4,-17/8),对称轴为x=-3/4
y=-3x²+2x+3
=(-3x²+2x)+3
=-3[x²-(2/3)x]+3
=-3[x²-(2/3)x+(1/3)²]+3+3×(1/3)²
=-3[x-(1/3)]²+10/3
抛物线的顶点坐标为(1/3,10/3),对称轴为x=1/3