Let x be the first integer, then
:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519
:
6x + 15 = 519
:
6x = 504
:
x = 84
:
*****************************
Our sequence is
:
84, 85, 86, 87, 88, 89
:
The third integer is 86
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
Hope this helps<span />
