Form 4 maths about function(2)

a. y = -0.005x^2+x
y = -0.005 ( x^2 + 200x )
y = -0.005 ( x^2 + 200x + 100^2 - 100^2 )
y = -0.005 ( x-100)^2 + 50

( This kind of calculation is called " Completing Square ". It can be used to find the maximum or minimum value of something.It depends on the coefficient of " a " whether it is positive or negative. When you face the question which requires you to rewrite an equation in the form y=a(x-h)^2 +k , you should find the common factor at first.In usual , the coefficient of " x^2 " should become 1. It is because of the convenience in calculation. Take (a) as an example , the common factor is -0.005 , so the coefficient of " x^2 " and " x" are 1 and 200 respectively. )

b. By (a) , the maximum height is 50m.

c. When y = 0 ,
0 = -0.005( x - 100 )^2 + 50
-50= -0.005 ( x -100 )^2
10000 = ( x-2 )^2
x = 200
so the target from the muzzle of the tank is 200m.

I am sorry that I forgot how to explain the question (d). I think I need to peply you about it later.

2008-10-14 22:14:37 補充：
reply , not " peply " , sorry ^^

y = -0.005x^2 + x
= -0.005(x^2 - 200x)
= -0.005[(x - 100)^2 - 10000]
= -0.005(x - 100)^2 + 50
So the max. height = 50.
Put y = 0
-50/-0.005 = (x - 100)^2
10000 = (x - 100)^2
+/-100 = x - 100
x = 0 or 200. So target is 200m from muzzle.
Adjusting the angle will change the equation of the path.