Which polynomial function best represents the four ordered pairs given in the example?
Reminder: The ordered pairs are (1, 6); (2, 11); (4, 39); and (7, -54).
A)x3 + 8x2 + 10x - 1 = f(x)
B)x3 - 4x2 + 10x - 1 = f(x)
C)-2x3 + 17x2 - 32x + 23 = f(x)
D)-2x3 - 17x2 - 23x + 32 = f(x)
+130474 We can do this one by process of elimination.
Add all the coefficents of each polynomial together....eliminate any whose sum is not 6.
This ....A and D can be eliminated (do you see why this is true??)
So the choice comes down to B or C
Note that when we put 7 into B, that the first term is a relatively larger positive to the second term's negative and the same is true of the third and 4th terms.....thus f(7) would be positive. But our f(7) has a negative value (-54).
Thus....C must be the correct answer.....
Here's the graph.......https://www.desmos.com/calculator/jsbsapxr1a
+23254 To figure this out:
take the first function: f(x) = x³+ 8x² + 10x - 1 and the first point: (1, 6)
find f(1) = (1)³+ 8(1)² + 10(1) - 1 = ?
If this answer isn't 6, this can't be the correct answer, so eliminate it and go to the next function.
If this answer is 6, then check out (2,11) and then (4, 39) and, finally, (7, -54).
If all four points work, that is the correct answer; if any one doesn't work, it can't be the right answer, go to the next function.
+130474 We can do this one by process of elimination.
Add all the coefficents of each polynomial together....eliminate any whose sum is not 6.
This ....A and D can be eliminated (do you see why this is true??)
So the choice comes down to B or C
Note that when we put 7 into B, that the first term is a relatively larger positive to the second term's negative and the same is true of the third and 4th terms.....thus f(7) would be positive. But our f(7) has a negative value (-54).
Thus....C must be the correct answer.....
Here's the graph.......https://www.desmos.com/calculator/jsbsapxr1a
