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? (5 points) part b: determine the x-intercepts. what do these values mean in the context of the problem? (5 points)

The vertex is either the maximum or minimum value
since the leading coefinet is negative (the number in front of the x² term), the parabola opens down and is a maximum

so
A.
a hack version is to use the -b/(2a) form
if  you have f(x)=ax²+bx+c, then the x value of the vertex is -b/(2a)
so
given
f(x)=-1x²+16x-60
the x value of the vertex is -16/(2*-1)=-16/-2=8
the y value is f(8)=-1(8)²+16(8)-60=
-1(64)+128-60=
4
the vertex is (8,4)
so you selll 8 candels to make the max profit which is $4

B.
x intercepts are where the line crosses the x axis or where f(x)=0
solve
0=-x²+16x-60
0=-1(x²-16x+60)
factor
what 2 numbers multiply to get 60 and add to get -16
-6 and -10
0=-1(x-6)(x-10)
set each factor to 0
0=x-6
x=6

0=x-10
10=x
x intercepts are at x=6 and 10
that is where you make 0 profit