Answer:
c = 5
Step-by-step explanation:
We can find a, b, c by filling in values from the table into the equation:
17 = a(2²) +b(2) +c
32 = a(3²) +b(3) +c
53 = a(4²) +b(4) +c
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There are numerous ways to solve 3 linear equations in 3 unknowns. We can use elimination.
Subtracting the first equation from each of the other two, we get ...
15 = 5a +b . . . . . . . . . note that c has been eliminated from the equations
36 = 12a +2b
Subtracting twice the first from the second gives ...
(12a +2b) -2(5a +b) = 36 -2(15)
2a = 6
a = 3
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Now that we have a value for "a", we can "back substitute" into the equations to find "b" and "c".
Substituting this into 15 = ..., we get ...
15 = 5(3) +b
0 = b
And substituting for "a" and "b" in the first original equation gives ...
17 = 4(3) +c
5 = c
The value of c, the constant of the function, is 5.
