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vladimir1956 [14]
3 years ago
5

The product of 2 consecutive odd integers is 1 less than 4 times their sum. A quadratic function models this situation. What is

the domain of the situation?
A) all integers
B) all odd integers
C) all odd numbers less than zero
D) all odd integers greater than zero
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
8 0
<span>Let the 2 consecutive odd integers be represented by:
 "x" and "(x+2)
_________________
The product of these two consecutive odd integers is:
________________
</span>→  <span>x*(x + 2); or, write as: x(x + 2)
__________________
The sum </span>of these two consecutive odd integers is:
<span>________________________________
</span>→  <span>x + (x + 2) = (2x + 2)
_______________________________
The product of 2 conductive integers, "</span>x(x + 2)" , is 1 less than 
   4 times their sum, "(2x + 2)".
<span>______________________________
</span>→  Write as: 4*(2x + 2) − 1 = x(x + 2)
<span>________________________________
Note the distributive property of multiplication:
_______________________________
</span>→  <span>a*(b + c) = ab + ac ;
________________________________
We have: 
___________
</span>→  4*(2x + 2) − 1 = x(x + 2)
<span>_____________________________
</span>      → 4*(2x + 2) = (4*2x)  + (4*2) = 8x + 8
<span>____________________________________
On the "right side of the equation; we have:
______________________________________
</span>→  x(x + 2) = (x*x) + (x*2) = x² + 2x
<span>_____________________________________
We can rewrite the equation:
__________________________
</span>→  4*(2x + 2) − 1 = x(x + 2) ;
<span>___________________________
by substituting our obtained "expanded values" for:
   "[</span>4*(2x + 2)]" ; and for: "[x(x + 2)]" ;
<span>______________________________________
</span>→  4*(2x + 2) − 1 = x(x + 2) =
____________________________
         →  8x + 8 − 1 = x² + 2x ;
__________________________________
→ Simplify the "+8 − 1" on the "left-hand side" of the equation to "7"; and subtract "2x" from EACH SIDE of the equation:
<span>____________________________________
</span>→  8x + 7 − 2x = x² + 2x − 2x ; to get:
<span>____________________________
</span>       → 6x + 7 = x² ;
________________________________
→To solve for "x";  Subtract "6x" and subtract "7"; from EACH SIDE of the equation; to get an equation in "quadratic format" ; that is:
<span>_____________________________________________
ax

let x and x+2 be the consecutive odd integers. Their product is x(x+2) Their sum is x + x+2 or 2x+2 x(x+2)=4(2x+2)-1 Domain is odd integers</span>
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