The table shows some values of a function of the form y = ax2 + bx + c.

The value of c, the constant of the function, is .

  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

__

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

__

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.