# What is the best way to graph this function?

I was given $R(x)=-1.5x^2+250x$ which represents the game systems sold and $C(x)=80x+150$ representing the cost to produce them. The restriction for $R(x)$ is $0 \leq x \leq 166$ and the restriction for $C(x)$ is $x \geq 0$.

I was also given the the equation for the profit which was $P(x)=R(x)-C(x)$, and the answer that I got was $P(x)=-1.5x^2+170x-150$.

Now I have to graph $y=P(x)$. I would just appreciate some suggestions on how to approach this or where to begin and what to find.

• You want to plot by hand or by computer? – polfosol Feb 7 '17 at 6:58
• @polfosol by hand:) assuming that I calculated the profit function correctly. – coderrr Feb 7 '17 at 7:00
• If you complete the square, it becomes much more clear what the graph of your quadratic function looks like. – littleO Feb 7 '17 at 7:04
• @littleO I tried completing the square just now and I ended up with numbers in the thousands... Does this seem right? – coderrr Feb 7 '17 at 7:08

Completing the square, we get, $$P \left(x\right) = -1.5 \left(x^2 -\frac {340}{3}x +100\right)$$ $$= -1.5 \left(\left(x-\frac {170}{3}\right)^2 -\left(\frac {170}{3}\right)^2 +100\right)$$ $$= -1.5 \left(\left(x-\frac {170}{3}\right)^2 -\frac {28000}{9}\right)$$ Hope you can take it from here.