C) the function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles 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? part
b.determine the x-intercepts. what do these values mean in the context of the problem?
Given the function modeling the profit: f(x)=-x^2+16x-60
a)a.determine the vertex. what does this calculation mean in the context of the problem? The vertex form is given by y=(x-h)^2+k, where (h,k) is the vertex: y=f(x)=-x^2+16x-60 y=x^2-16x+60 c=(-b/2a)^2 b=16 thus c=(-16/2)^2=64 hence: y=x^2-16x+64+60-64 y=(x-8)(x-8)-4 y=(x-8)^2-4 hence the vertex form will be: y=(x-8)^2-4 the vertex is (8,-4) The vertex represents the highest point of the graph which is the highest daily profits attained.
b] determine the x-intercepts. what do these values mean in the context of the problem? let y=0 thus 0=−x2 + 16x − 60 factorizing the above we get: 0=x^2-16x+60 0=x^2-6x-10x+60 0=x(x-6)-10(x-6) thus x=6 and x=10 thus the x-intercepts are x=6 and x=10, they represent the breakeven point. The minimum number of units they can sell and not make any profit
