(09.02 hc)
the function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships sold and f(x) is the amount of profit.
part a: determine the vertex. what does this calculation mean in the context of the problem? (5 points)
part b: determine the x-intercepts. what do these values mean in the context of the problem?

We factor the equation to get:

-(x-25)^2+361

In the form a(x-h)^2+k, the vertex is (h, k), so the vertex is (25, 361).  This means that the studio makes the most profit from selling 25 memberships, and thus makes 361 dollars.

B.  The x-intercepts are the values of x for which f(x) is 0.  This equation can be factored as (-a+6)(a-44)=0, with solutions 6 and 44.  Therefore, by selling either 6 memberships or 44 memberships, the studio breaks even, neither making nor losing money.

Agc and bgd are vertical angles