Question

the power generated by an electrical circuit (in watts) as a function of its current ( x ) (in amperes) is modeled by ( p(x)=-15x(x - 8) ). what current will produce the maximum power? amperes

Explanation:

Step1: Expand the function

$$\begin{align*} P(x)&=-15x(x - 8)\\ &=-15x^{2}+120x \end{align*}$$

Step2: Find the axis of symmetry

For a quadratic function \(y = ax^{2}+bx + c\), the formula for the axis of symmetry is \(x=-\frac{b}{2a}\). Here \(a=-15\) and \(b = 120\).

$$ x=-\frac{120}{2\times(-15)} $$

Step3: Calculate the value of \(x\)

$$ x = 4 $$

Answer:

\(4\)