SOLUTION: TR= -60p2 + 240p

Question 228691: TR= -60p2 + 240p
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
If you want the maximum value of this function, there are a couple of ways to find it. And, when you get to CALCULUS, there will be an even EASIER way to do it! For now, I'll show you METHOD I (Graphing Calculator) and METHOD II (Vertex at x=-b/(2a) method!)

METHOD I: Graph the function y=-60x^2+ 240x with a graphing calculator (or the old-fashioned way by just plotting points, realizing that a graph in this form with the x^2 with a negative coefficient is a parabola opening downward!)

Of course, if you graph this with a standard window, it won't even look like a parabola--it looks like a line. So you need a "larger" window on the calculator. This is a trial and error process to decide what x and y values will give you the best looking graph. You might want to start by finding the x-intercepts. Let y=0, and solve -60x^2 + 240x = 0. Factor the common factor of -60x, which leaves -60x(x-4)=0. The x intercepts are at x=0 and x=4, so I recommend that you make your calculator x window go from, let's say, x=-4 to x=6. Then notice that the graph goes way off the top of the graph. So use larger values of y, like y=-100 to y=100. The graph still goes way off the top of the graph, so it turns out that y=-100 to y=300 looks pretty good. Here is what your graph should look like:

Now that you have the graph, you can probably see that the maximum point of the graph is at x=2. If x=2, plug it back into the formula and get y=-60*2^2+240*2, which is y=240 for the maximum value. You can also get this directly from the calculator using the TRACE button (if you have a TI83 or TI84!), or the "Maximum/Minimum" function if you know how to use that.

By the way, if ANYONE needs help with a TI calculator, send me an Email at rapaljer@scc-fl.edu, and I'll send you (free, of course!) a link to the page on my website explaining TI graphing calculators -- I made it a LOT easier than that HUGE book that came with your calculator!

METHOD II: Find the vertex using the method.
It turns out that the vertex of a parabola is at the point where .

In this case so a=-60 and b=240, so

If x=2, then

Which method do you like?? Anyone can send me an Email at rapaljer@scc-fl.edu.

Dr. Robert J. Rapalje
Seminole State College of Florida
Altamonte Springs Campus
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