The quick computing company discovered that it costs 45$ to produce 2 calculators, 143$ to produce 4 calculators, and 869$ to produce 10 calculators.
find the total cost of producing 7 calculators?

Using the points (2, 45) (4, 143) and (10, 869), we can plug them into the following system of 3 equations using the y = ax^2 + bx + c format:

45 = a(2)^2 + b(2) + c
143 = a(4)^2 + b(4) + c
869 = a(10)^2 + b(10) + c

which simplifies to:

45 = 4a + 2b + c
143 = 16a + 4b + c
869 = 100a + 10b + c

Solving the system, we get a = 9, b = -5, and c = 19. Thus the equation is:

c(x) = 9x^2 - 5x + 19

If you have a TI graphing calculator, you can also enter the points by pressing Stat -> Edit and enter (2, 45) (4, 143) and (10, 869) into it. Go back and calculate the QuadReg of the points from the Calc tab and it will give you the same answer.

Now that we know the function that will produce the price of production for any number of calculators, plug in x = 7 and it will give you the price to produce 7 calculators.

c(x) = 9x^2 - 5x + 19
==> c(7) = 9(7)^2 - 5(7) + 19
==> c(7) = 441 - 35 + 19
==> c(7) = 425

Therefore, it costs $425 to produce 7 calculators.

Hope this helps.