F4 Math一問~~~~~

y = ax2 + bx + c

Since the equation passes through the origin.

So, sub (0 , 0) into the equation,

We get, c = 0

Since the equation passes through (8 , 0)

So, sub (8 , 0) into the equation,

We get, 0 = a(8)2 + b(8)

b = -8a

Since the equation passes through (2 , 3)

So, sub (2 , 3) into the equation,

We get, 3 = a(2)2 + b(2)

3 = 4a + 2(-8a)

3 = -12a

a = -1/4

b = 2

put (0,0) in y=ax^2+bx+c we get c = 0
put (2,3) and (8,0) in y=ax^2+bx+c we get
64a+8b=0 => 8a+b =0 .... (a) (c=0)
4a+2b =3 ..... (b)
(b)*2 -(a) we get 3b = 6 => b =2

put b=2 into (a) 8a+2=0 => a=-1/4

y=ax^2+bx+c ==> y=-1/4x^2+2x

The equation y = ax^2 + bx + c cuts at origin
Therefore put (0,0) into the equation
0 = a(0^2) + b(0) + c
c = 0

This passes through (2,3), put (2,3) into the equation y = ax^2 + bx
3 = a(2)^2 + b(2)
3 = 4a + 2b -- (1)
This passes through (8,0), put (8,0) into the equation y = ax^2 + bx
0 = a(8^2) + b(8)
0 = 64a + 8b
0 = 8a + b -- (2)

From (2)
0 = 8a + b
b = -8a
Put b = -8a into (1)
3 = 4a + 2(-8a)
3 = 4a - 16a
3 = -12a
a = -1/4

Put a = -1/4 into b=-8a
b = -8(-1/4)
b = 2

Therefore, a=-1/4, b=2, c=0