Posted by T.Gracken on August 19, 2002 at 11:54:10:
In Reply to: Re: what do you mean? posted by susan on August 18, 2002 at 23:05:43:
O.K. to write y= lx^2-3x+2l + lx^2-5x-14l - 3x + 1 without absolute values,
start by determining when each absolute value expression is positive, negative, or zero.
for lx^2-3x+2l, you should get x^2-3x+2 is positive on (-inf,1) and (2,inf), negative on (1,2)
for lx^2-5x-14l, you should get x^2-5x-14 is positive on (-inf,-2) and (7,inf), negative on (-2,7)
so consider the following intervals: (-inf,-2), (-2,1), (1,2), (2,7), and (7,inf).
using the definition of absolute value,
when x^2-3x+2 is positive, lx^2-3x+2l = x^2-3x+2,
when x^2-3x+2 is negative lx^2-3x+2l = -x^2+3x-2,
when x^2-5x-14 is positive, lx^2-5x-14l = x^2-5x-14, and
when x^2-5x-14 is negative lx^2-5x-14l = -x^2+5x+14.
{(because of html) i will use =< to mean less than or equal to.}
using the intervals above, you can rewrite the function as
y =
2x2 - 11x - 11 ...if x =< -2
-x + 17 ................................if -2 < x =< 1
-2x2 + 5x + 13 ...if 1 < x =< 2
-x + 17 ................................if 2 < x =< 7
2x2 - 11x - 11 ...if x > 7
hope that helps.