Question

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=

Answer 1

Answer:

  y = 7x²

Step-by-step 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).