Question

已知三点坐标,求抛物线方程,比如(15,20.3) (35,30.7 )( 50,36.6),

Answer 1

y=ax²+bx+c

所以

225a+15b+c=20.3 (1)

1225a+35b+c=30.7 (2)

2500a+50b+c=36.6 (3)

(2)-(1)

1000a+20b=10.4

所以50a+b=0.52 (4)

(3)-(2)

1275a+15b=5.9

所以85a+b=59/150 (5)

(5)-(4)

35a=-19/150

a=-19/5250

b=59/150-85a=368/315

c=20.3-225a-15b=377/105

所以y=-19x²/5250+368x/315+377/105