Geo5.1.8

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Find the equation of the parabola whose axis is parallel to Y-axis and passing through (2,5),(1,4),(-1,8)\,

The equation of the parabola whose axis is parallel to y axis is y=lx^{2}+mx+n\,

The parabola passes through (2,5),(1,4),(-1,8)\,

5=4l+2m+n,4=l+m+n,8=l-m+n\,

3l+m=1,2m=-4,m=-2,l=1,n=-5\,

Therefore,the equation is

y=x^{2}-2x-5\,


Main Page:Geometry:The Parabola