5. the amount of profit bill makes per toy when he increases or decreases the price of his handmade toys can…

5. the amount of profit bill makes per toy when he increases or decreases the price of his handmade toys can be modeled by the function (f(x)=-x^{2}-2x + 3). what price change gives him the highest profit? what is highest profit per toy? price change: blue - box maximum profit per toy: $blue - box

5. the amount of profit bill makes per toy when he increases or decreases the price of his handmade toys can be modeled by the function (f(x)=-x^{2}-2x + 3). what price change gives him the highest profit? what is highest profit per toy? price change: blue - box maximum profit per toy: $blue - box

Answer

Explanation:

Step1: Identify the function type

The profit function $f(x)=-x^{2}-2x + 3$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-1$, $b=-2$, $c = 3$.

Step2: Find the x - value of the vertex

The x - value of the vertex of a quadratic function $y=ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting $a=-1$ and $b = - 2$ into the formula, we have $x=-\frac{-2}{2\times(-1)}=-1$. This is the price - change that gives the highest profit.

Step3: Find the maximum profit

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

Answer:

Price change: - 1 Maximum profit per toy: $4$