Q:

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=

Accepted Solution

A:
Answer:   y = 7x²Step-by-step explanation:One clue that the relation is quadratic is found in the second differences:First differences are ...7 -0 = 728 -7 = 2163 -28 = 35112 -63 = 49Then second differences are ...21 -7 = 1435 -21 = 1449 -35 = 14These 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 = 0for x=1, y = 7·1² = 7for x=2, y = 7·2² = 28for x=3, y = 7·3² = 63for x=4, y = 7·4² = 112A rule that represents the function is y = 7x²._____Alternate solutionAnother way you might approach this is to factor the y-values:for x=0, y = 0for x=1, y = 7·1for x=2, y = 7·2·2for x=3, y = 7·3·3for 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).