Answer:
y = 7x²
Explanation:
One clue that the relation is quadratic is found in the second differences:
First differences are ...
- 7 -0 = 7
- 28 -7 = 21
- 63 -28 = 35
- 112 -63 = 49
Then second differences are ...
- 21 -7 = 14
- 35 -21 = 14
- 49 -35 = 14
These are constant, indicating the function is 2nd-degree, or quadratic. The coefficient of the x² term is half the value of these second differences, so it will be 7.
When we compare y = 7x² with the given relation values, we find that no additional adjustment is needed in this rule.
- for x=0, y = 7·0² = 0
- for x=1, y = 7·1² = 7
- for x=2, y = 7·2² = 28
- for x=3, y = 7·3² = 63
- for x=4, y = 7·4² = 112
A rule that represents the function is y = 7x².
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Alternate solution
Another way you might approach this is to factor the y-values:
- for x=0, y = 0
- for x=1, y = 7·1
- for x=2, y = 7·2·2
- for x=3, y = 7·3·3
- for x=4, y= 7·4·4 or 7·2·2·2·2 (the first form is more recognizably a part of the pattern y = 7x²).