The vertex is the minimum or maximum point of a parabola.
The formula to find the vertex is, where a, b and c are values in the standard form of quadratic equation is:
x min/max = - b / 2a
If a > 0, then the parabola the y-value of the vertex is the minimum value of the function.
If a < 0, then the parabola the y-value of the vertex is the maximum value of the function.
The formula to find the vertex is, where a, b and c are values in the standard form of quadratic equation is:
x min/max = - b / 2a
If a > 0, then the parabola the y-value of the vertex is the minimum value of the function.
If a < 0, then the parabola the y-value of the vertex is the maximum value of the function.
In your case:
c(x) = 0.3 x² - 96 x + 26 919
a = 0.3 , b = - 93 , c = 26 919
a > 0 , so the y-value of the vertex is the minimum value of the function.
x min = - b / 2a = - ( - 96 ) / 2 ∙ 0.3 = 96 / 0.6 = 160
160 engines must be made to minimize the unit cost.
c min = c ( 160 ) = 0.3 ∙ 160² - 96 ∙ 160 + 26 919 = 19 239