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The set of ordered pairs represents a function. Write a rule that represents the function.

​(0​,0​), ​(1​,7​), ​(2​,28​), ​(3​,63​), ​(4​,112​)

y=

User Max Oriola
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3 votes

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.

_____

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).
User Jaromir Hamala
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8.0k points

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