Question

已知抛物线y=六分之一（X-2）（x-2t-3）（t大于0）与X轴交于点A,B（在A的左边）与y轴交与点C

Answer 1

(1)

y= (1/6)(x-2)(x-2t-3)

y =0

=> x= 2 or 2t+3

A(2t+3,0),B(2,0)

x=0

y=(1/6)(-2)(-2t-3)=(1/3)(2t+3)

C(0,(1/3)(2t+3))

(2)

|AB| = 2t+1

|OC| = (1/3)(2t+3)

△ABC的面积= 21/2 = (1/2)|AB||OC|

=>21/2 = (1/6)(2t+3)(2t+1)

63= 4t^2+8t+3

t^2+2t-15 =0

(t+5)(t-3)=0

t= 3 or -5(rejected)

y= (1/6)(x-2)(x-2t-3)

= (1/6)(x-2)(x-9)