the function f(x)=-(x - 20)(x - 100) represents a companys monthly profit as a function of x, the number of…

the function f(x)=-(x - 20)(x - 100) represents a companys monthly profit as a function of x, the number of purchase orders received. which number of purchase orders will generate the greatest profit?\n20\n60\n80\n100

the function f(x)=-(x - 20)(x - 100) represents a companys monthly profit as a function of x, the number of purchase orders received. which number of purchase orders will generate the greatest profit?\n20\n60\n80\n100

Answer

Explanation:

Step1: Expand the function

$f(x)=-(x - 20)(x - 100)=-(x^{2}-100x - 20x+2000)=-x^{2}+120x - 2000$

Step2: Identify the coefficients

For a quadratic function $y = ax^{2}+bx + c$, here $a=-1$, $b = 120$, $c=-2000$.

Step3: Use the formula for the x - coordinate of the vertex

The x - coordinate of the vertex of a quadratic function $y=ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. Substitute $a=-1$ and $b = 120$ into the formula: $x=-\frac{120}{2\times(-1)} = 60$.

Answer:

B. 60