f.4 mathz..

Let f(x) = x(2x﹣5)(x﹣1) + 3
The original function : y = x(2x﹣5)(x﹣1) + 3
When the graph is translated 1 unit to the left,
the function will become : f(x + 1)
f(x + 1)= (x + 1) [2(x + 1)﹣5] [(x + 1)﹣1] + 3
 = (x + 1)(2x + 2﹣5)(x + 1﹣1) + 3
 = (x + 1)(2x﹣3)(x) + 3

When the graph is reflected in the x-axis,
the f(x + 1) = -f(x + 1)

Therefore, after the transformation,
the function will become :
-f(x + 1) = -[(x + 1)(2x﹣3)(x) + 3]
= -(x + 1)(2x﹣3)(x)﹣3
= (x + 1)(3﹣2x)(x)﹣3

2008-10-19 21:13:50 補充：
當然，你亦可以展開
-f(x + 1)
= (x + 1)(3﹣2x)(x)﹣3
= x(3x﹣2x^2 + 3﹣2x)﹣3
= x(x﹣2x^2 + 3)﹣3
= x^2﹣2x^3 + 3x﹣3
= -2x^3 + x^2 + 3x﹣3

2008-10-19 21:32:04 補充：
有不明白的地方，歡迎發問。

2008-10-24 16:31:55 補充：
通當都是以展開左的形式表達 function
即 -f(x + 1) = -2x^3 + x^2 + 3x﹣3

f(x) = x(2x-5)(x-1) 3
f(x 1) = (x 1)(2x 2-5)x 3
-f(x 1) = -x(x 1)(2x-3)-3
so
y =-x(x 1)(2x-3)-3
y =-x(2x^2-x-3)-3
y =-2x^3 x^2 3x -3

Hope I can help you.

f(x) = x(2x-5)(x-1)+3

when translated 1 unit to the left
f(x+1) = (x+1)(2x+2-5)x+3

when reflected in the x-axis
-f(x+1) = -x(x+1)(2x-3)-3

the equation
y =-x(x+1)(2x-3)-3
y =-x(2x^2-x-3)-3
y =-2x^3 +x^2 +3x -3