The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, 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

For letter A, we are asked to determine the vertex of the given function. First, we need to identify each value such as:
a = -1
b = 20
c = -75
The formula in determining the vertex (h, k) is h = -b / 2a
Solving for h, we have it:
h = - 20/ 2*(-1)
h = -20 /-2
h = 10
Solving for k, we have it:
f(h) = -1*10² + 20*10 - 75
f(h) = -100 + 200 - 75
f(h) = 25
Therefore, the vertex is (10,25)
since value for a is negative, the vertex is the maximum point such as when you have 10 photos, you will get $25 profit

For letter B, solving for x-intercepts, we have it:
0 = -1x² + 20x - 75 , divide both sides by -1
0 = x² - 20x + 75
0 = (x-15) (x-5)
x1 = 15
x2=5
If these values are the number of photos, there will be no profit. Break even.