The expression 8x - x^2 can be written in the form p - (x - q)^2, for all values of x.
How do you find the value of p and the value of q? Please explain simply and in detail.
2007-04-23 04:44:39 · 4 answers · asked by mbchelsea 1 in Science & Mathematics ➔ Mathematics
I have no idea.
2007-04-23 04:51:43 · answer #1 · answered by Nyce_Nay 3 · 0⤊ 0⤋
p - ( x -q) ^ 2 = p - x^2 - q^2 + 2xq
For 8x - x^2 to be written as p - ( x -q) ^ 2
The expression p - x^2 - q^2 + 2xq should be equal to 8x - x^2
Comparing the coefficients of x ^ 0 (i.e. constants), x, x^2, we get
p - q^2 =0 => p = q^2
2q = 8 => q = 4
Thus p = 16.
2007-04-23 04:52:30 · answer #2 · answered by Anonymous · 1⤊ 0⤋
you need to complete the square
-(x^2-8x)
=-(x^2-8x+16-16)
= (- (x-4)^2-16)
=16-(x-4)^2)
to get to the 16 you say (x-c)^2=x^2-2XC+c^2
therfore the end term c= -8x/-2x=4
4^2=16
But you cant change the expression so when you add the 16 you must subtract it again
2007-04-23 04:51:50 · answer #3 · answered by Anonymous · 0⤊ 1⤋
= - (x² - 8x)
= - (x² - 8x + 16 - 16)
= - (x - 4)² + 16
= 16 - (x - 4)²
p = 16 , q = 4
2007-04-23 04:55:01 · answer #4 · answered by Como 7 · 1⤊ 0⤋