The function f(x) = −x^2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold. Determine the vertex, and explain what it means in the context of the problem.
This is a dome shaped parabola (due to the negative coefficint of x^2)
the max will occur at x = -b/2a b = 16 a = -1 so max is at x = 8
sub in x = 8 in the equation to find the max value of the quadratic function
- 8^2 + 16(8) - 60 = 4 this is the max daily profit....found when you sell a measly 8 candles !
Here is a graph of the fxn: