The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling donut combos, where x is the number of combos 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)

Can someone please help me

Question

The function f(x) = −x2 + 44x − 384 models the daily profit, in dollars, a shop makes for selling donut combos, where x is the number of combos 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)


Can someone please help me

anonymous · Answer

A. 
$$-(x^{2}-44x +484-484+384)$$
$$-(x-22)^{2}+100$$
Vertex is (22,100)
Since the equation is in the form -(x-a)^2 +b, meaning the vertex is the maximum point of the curve.
Relating to the situation, it just means that 100 is the maximum profit and 22 is the corresponding number of combos sold

B. To get the x-intercepts, just factor it out.
x-int is (x,0)
so. 0=(x-32)(X-12)
x-intercepts are 12 and 32
in these points, f(x)=0 which means the profit is also zero.


Just a trick to check if we're correct, see how the the average of the 2 x-intercepts equates to the x of the vertex? since vertex can also correspond to the axis of symmetry