6. the amount of profit bill makes per toy when he increases or decreases the price of his han be modeled by…

6. the amount of profit bill makes per toy when he increases or decreases the price of his han be modeled by the function ( f(x)=-x^{2}-2x + 3 ). what price change gives him the highest profit per toy? (8pts) show work!!! price change: $ maximum profit per toy: $

6. the amount of profit bill makes per toy when he increases or decreases the price of his han be modeled by the function ( f(x)=-x^{2}-2x + 3 ). what price change gives him the highest profit per toy? (8pts) show work!!! price change: $ maximum profit per toy: $

Answer

Explanation:

Step1: Find the vertex of the quadratic function

The function (f(x)=-x^{2}-2x + 3) is a quadratic function in the form (y = ax^{2}+bx + c), where (a=-1), (b = - 2), (c = 3). The (x) - coordinate of the vertex of a quadratic function (y=ax^{2}+bx + c) is given by (x=-\frac{b}{2a}). Substitute (a=-1) and (b=-2) into the formula: (x=-\frac{-2}{2\times(-1)}=\frac{2}{-2}=-1)

Step2: Find the maximum value of the function

Substitute (x = - 1) into the function (f(x)=-x^{2}-2x + 3) (f(-1)=-(-1)^{2}-2\times(-1)+3) (=-1 + 2+3) (=4)

Answer:

Price change: (-1) (This means a price decrease of ($1)), Maximum profit per toy: (4)