SOLUTION: What is the answer to the algebraic pattern below and how did you get to this answer. This is homework for my son. Please show work. x,-1,0,-2,1,2 y,-1,0,-8,1,8

Question 390803: What is the answer to the algebraic pattern below and how did you get to this answer. This is homework for my son. Please show work.
x,-1,0,-2,1,2
y,-1,0,-8,1,8
Found 3 solutions by stanbon, haileytucki, richard1234:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
What is the answer to the algebraic pattern below and how did you get to this answer. This is homework for my son. Please show work.
x,-1,0,-2,1,2
y,-1,0,-8,1,8
-----
Ans: y = x^3
==================
Cheers,
Stan H.
Answer by haileytucki(390)   (Show Source): You can put this solution on YOUR website!
well, you can find the midpoint by:
x(-1,0,-2,1,2)_y(-1,0,-8,1,8)
Use the midpoint formula to find the midpoint of the line segment.
((x1+x2)/(2) , (y1+y2)/(2))
Substitute in the values for (x1,y1) and (x2,y2).
((-1-1)/(2),(0+0)/(2))
Subtract 1 from -1 to get -2.
((-2)/(2),(0+0)/(2))
Move the minus sign from the numerator to the front of the expression.
(-(2)/(2),(0+0)/(2))
Reduce the expression -(2)/(2) by removing a factor of 2 from the numerator and denominator.
(-1,(0+0)/(2))
Combine all similar expressions.
(-1,(0)/(2))
Reduce the expression (0)/(2) by removing a factor of from the numerator and denominator.
(-1,0)

Or find the equation using the two points (x,y)
x(-1,0,-2,1,2)_y(-1,0,-8,1,8)
Use y=mx+b to calculate the equation of the line, where m represents the slope and b represents the y-intercept.
To calculate the equation of the line, use the y=mx+b format.
Slope is equal to the change in y over the change in x, or 'rise over run'.
m=(change in y)/(change in x)
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=(y2-y1)/(x2-x1)
Substitute in the values of x and y into the equation to find the slope.
m=(0-(0))/(-1-(-1))
Multiply -1 by each term inside the parentheses.
m=(0-(0))/(-1+1)
Add 1 to -1 to get 0.
m=(0-(0))/(0)
Since the denominator is 0, the slope is undefined.
Undefined
The slope is undefined, so this is the equation of a vertical line.
x=-1

Answer by richard1234(7193)   (Show Source): You can put this solution on YOUR website!
Put the coordinates in order first:

(-2, -8)
(-1, -1)
(0, 0)
(1, 1)
(2, 8)

Very likely that the function is . How I got to this answer -- just realize that -8 = (-2)^3, -1 = (-1)^3, etc. I cannot be certain that since it's quite possible to define an unusual function that satisfies all the constraints.
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