F4 Maths FUnctions and Graphs

Jacky0509

1. Given that axis of symmetry of the function y= -x^2+4kx+k^2 is x= -5, find
(a) the value of k,
(b) the maximum value of the function.

2. Given that the minimum value of the function y= 2x^2+6x+( k^2+8k-1) is 3.5, find
(a) the values of k,
(b) the axis of symmetry of the function.

3. Find two integers whose difference is 50, such that the sum of the square of the smaller integer and 20 times the larger integer is a minimum.

4. Find two integers whose sum is 60, such that the difference between the square of the larger integer and twice the square of the smaller integer is a maximum.

Please have a help, thanks for every one~~

[S]【YU】

1)
discriminant > 0 --> 2 distinct real roots
sum of root/2  = 4k/2 = -5
k = -2.5

2) By method of completing square
y= 2x^2+6x+( k^2+8k-1)
= 2(x^2+3x) + ( k^2+8k-1)
= 2[x^2 + 3x + (3/2)^2] - 2(3/2)^2 + ( k^2+8k-1)
= 2(x+3/2)^2 + (k^2 + 8k - 5.5)

(k^2 + 8k - 5.5) = 3.5
k = 1 , -9
axis of symmetry: x = -3/2

let x be the larger number
3. find the min of  20x^2 + (50 -x)^2

4. find the max of  x^2 - 2(60 -x)^2

Jacky0509

1)
discriminant > 0 --> 2 distinct real roots
sum of root/2  = 4k/2 = -5
k = -2.5

2) By method of completing square
y= 2x^2+6x+( k^2+8k-1)
= 2(x^2+3x) + ( k^2+8k-1)
= 2[x^2 + 3x + (3/2)^2] - 2(3/2)^ ...
[S]【YU】 發表於 10-11-2009 23:05

Thx a lot ^^