The function f(x) = −x^2 + 44x − 384 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games 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? (5 points

Question

The function f(x) = −x^2 + 44x − 384 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games 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? (5 points

whpalmer4 · Answer

This is a parabola:
$$y = ax^2 + bx + c$$
The vertex of a parabola written in that form can be found to be
$$x = -\frac{b}{2a},\ y = f(x)$$in other words, find the $x$ value from the first formula, and plug it into the equation to get the $y$ value there.

The $x$-intercepts are the points where the parabola crosses the $x$-axis.  This is the same as solving for $x$ in $$f(x) = 0$$or$$-x^2+44x-384=0$$