Question

The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 - x box seats. The function S = 50x - x2 gives the estimated income from the sale of box seats. Graph the function, and use the graph to find the price for box seats that will give the greatest income.

Answer 1

the S function is \[S = 50x-x^2\]?

Make yourself a table of values:

x S
0 \(50(0)-0^2 = 0\)
1 \(50(1)-1^2 = 49\)
2 \(50(2)-2^2 =96\)
3 \(50(3)-3^2 = 141\)
...
48 \(50(48)-48^2 = 96\)
49 \(50(49)-49^2 = 49\)
50 \(50(50) - 50^2 = 0\)

then draw your graph. You might do a sketch with just a few points spread out to get an idea of the shape of the graph and then concentrate your points where it looks interesting, rather than compute all of the values.