Particle 1 moves along the path y=x^2-6x+8 from A(0,8) to B(5,3). Particle 2 moves along the path y=|x^2-6x+8| from A(0,8) to B(5,3). Which of the following describes the interval where the two particles are separated.
Answers
Given : Particle 1 moves along the path y=x^2-6x+8 from A(0,8) to B(5,3). Particle 2 moves along the path y=|x^2-6x+8| from A(0,8) to B(5,3).
To find : Which of the following describes the interval where the two particles are separated.
Solution:
y = x²- 6x + 8
=> y = x² - 4x - 2x + 8
=> y = x(x - 4) - 2(x - 4)
=> y = (x - 4)(x - 2)
x = 4 , x = 2
X < 2 y >0
2 < x < 4 y < 0
x > 4 y > 0
Hence between 2 & 4 y=|x²-6x+8| is + ve while x²-6x+8 is - ve
( 2, 4 ) is the interval where the two particles are separated.
y = x²- 6x + 8
A(0,8) to B(5,3).
x y
0 8
1 3
2 0
3 -1
4 0
5 3
y=|x^2-6x+8|
A(0,8) to B(5,3).
x y
0 8
1 3
2 0
3 1
4 0
5 3
( 2, 4 ) is the interval where the two particles are separated.
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