中四數學（英文）

1)
No any graph. How to find it? =,=

2)
α+β=-b/a=-4
αβ=c/a=-6

α^2+β^2=(α+β)^2 - 2αβ
=(-4)^2 - 2(-6)
=28

α^3+β^3 = (α+β)(α^2 - αβ + β^2)
=(α+β)(α^2 + β^2 - αβ)
=(-4)[(28)-(-6)]
=-136

∴The equation whose roots are α²+β² and α³+β³ are:
x^2 - (28-136)x + (28)(-136)
=x^2 + 108x - 3808

3a)
Put x=0 into 3x-4y=24.
3(0) - 4y=24
-4y=24
y=-6

∴B is (-6,0).

Put y=0 into 3x-4y=24
3x-4(0)=24
3x=24
x=8

∴A is (0,8).

∴The mid-point of AB: ( -6/2 , 8/2) = (-3,4)

3b)
3x-4y=24
3x-24=4y
y=3x/4 - 6

∵The slope of AB: 3/4
∴The slope of the perpendicular bisector of AB: -1/(3/4)=-4/3

∴The equation of the perpendicular bisector of AB:
-4/3 = (y-4)/(x+3)
-4x-12 = 3y-12
-4x=3y
4x+3y=0

4a)
∵The straight line whose x-intercept is half of its y-intercept.
Let the x-intercept be (x,0), then y-intercept is (0,2x)
The equation of the line:
(2x-0)/(0-x)=(y-3)/(x-5/2)
-2x/x = (y-3)/(x-5/2)
-2 = (y-3)/(x-5/2)
-2x+5 = y-3
2x+y-8=0

4b)
Put x=0 into 2x+y-8=0.
2(0)+y-8=0
y=8

∴The x-intercept is (4,0), then y-intercept is (0,8)

∴The area enclosed by the line and the positive axes:
4(8)/2
=16 sq. units

2015-01-01 19:49:36 補充：
The answer 3a,3b are wrong.

3a)
A is (8,0).
B is (0,-6).
∴The mid-point of AB: ( 8/2 , -6/2) = (4,-3)

3b)
∴The equation of the perpendicular bisector of AB:
-4/3 = (y+3)/(x-4)
-4x+16 = 3y+9
4x+3y-7=0

2015-01-01 21:59:50 補充：
1)
You need to give me a graph.
Btw,
y= - x^2 + 4x -3
aiii) ∵y=ax^2 + bx +c is the general fomula of quadratic equation and a is a negative number.
∴It is opening downwards.
y= -(x^2 - 4x) - 3
y= -(x^2 - 4x + 4) -3 + 4
y= -(x-2)^2 +1
ai)∴The axis of symmetry is x=2.

2015-01-01 22:03:58 補充：
佢唔比我再補充,我係意見答

2015-01-01 22:07:32 補充：
v)
Put y=0 into y=-x^2+4x-3.
- x^2 + 4x -3 = 0
(x-1)(x-3)=0
x=1 or x=3

∴The x-intercepts are (1,0) and (3,0).

1b)
∵The vertex is (2,1) and it is opening downwards.
∴The maximum value of y is 1 when x is 2.

2015-01-01 22:12:39 補充：
iv)
Put x=0 into y=-x^2+4x-3.
y=-(0)^2 +4(0) -3
y=-3

∴The y-intercept is (0,-3).

ii)
∵y= -(x-2)^2 +1
∴The coordinates of the vertex is (2,1).