Question 966145
2.2n^2 - 66n + 655 is a quadratic equation that opens up and points down.


the graph of that equation looks like this:


{{{graph(400,400,-50,50,-1000,1000,2.2x^2-66x+655)}}}}


the minimum point on the graph of that equation is found by the formula:


x = -b/2a


the quadratic formula in standard form is ax^2 + bx + c = 0


just replace n with x and your equation will conform to this convention.


2.2n^2 - 66n + 655 becomes 2.2x^2 - 66x + 655.


since this equation is in standard form, then:


a = 2.2
b = -66
c = 655


x = -b/2a becomes x = 66/4.4 which becomes x = 15


when x = 15, 2.2x^2 - 66x + 655 becomes 2.2(15)^2 - 66(15) + 655 which becomes 160.


the minimum point on the graph is when x = 15 and y = 160.


that can be seen on the same graph with y = 160 added to it as shown below:


{{{graph(400,400,-50,50,-1000,1000,2.2x^2-66x+655,160)}}}}


the question is:


For what number of minutes is the cost of running the machine a minimum? What is the minimum cost?


the answer is:


the minimum cost is 160 pesos when the machine has been running for 15 minutes.