Answer :
Answer:
5 amperes will produce the maximum power of 300 watts.
Step-by-step explanation:
The general form of a quadratic function presents the function in the form
[tex]f(x)=ax^2+bx+c[/tex]
The vertex of a quadratic function is the highest or lowest point, also known as the maximum or minimum of a quadratic function.
We can define the vertex by doing the following:
- Identify a, b, and c
- Find, the x-coordinate of the vertex, by substituting a and b into
[tex]x-coordinate =-\frac{b}{2a}[/tex]
- Find, the y-coordinate of the vertex, by evaluating
[tex]y-coordinate =f(x-coordinate )=f(-\frac{b}{2a} )[/tex]
We know that the power generated by an electrical circuit is modeled by
[tex]P(c)=-12c^{2}+120c[/tex]
This function is a quadratic function.
To find the current that produce the maximum power you must
- Identify a and b
a = -12 and b = 120
- Find, the maximum current of the vertex, by substituting a and b into
[tex]maximum-current =-\frac{b}{2a}[/tex]
[tex]maximum-current =-\frac{120}{2(-12)}\\\\maximum-current = 5[/tex]
- Find, the maximum-power, by evaluating
[tex]maximum-power =P(maximum-current)=P(-\frac{b}{2a} )[/tex]
[tex]P(5)=-12(5)^{2}+120(5)=300[/tex]
5 amperes will produce the maximum power of 300 watts.
We can check our work with the graph of the function [tex]P(c)=-12c^{2}+120c[/tex] and see that the maximum is (5, 300).
