A manufacturer of lighting fixtures has daily production costs of

Equation the function in quadratic form, ${\displaystyle f\left(x\right)=a{x}^2+bx+c}$ 
${\displaystyle C=0.25x^2-10x+800}$ 
The function has a minimum when ${\displaystyle x=-\frac{b}{2a}}$ since ${\displaystyle a>0}$. To produce a minimum cost, determine the quantity of fixtures that must be manufactured per day. Let ${\displaystyle a=0.25}$ and ${\displaystyle b=-10}$ 
${\displaystyle x=-\frac{b}{2a}}$ 
${\displaystyle x=-\frac{-10}{2\left(0.25\right)}}$ 
${\displaystyle x=-\frac{-10}{0.5}}$ 
${\displaystyle x=20}$ 
The manufacturer should produced 20 lighting fixtures daily to yield a minimum cost.

To yield a minimum cost, the number of fixtures that should be produced daily is ${\displaystyle x=-\frac{-b}{2a}}$. We are aware that ${\displaystyle a=0.25}$ and ${\displaystyle b=-10}$ 
Let's calculate that x's value:
${\displaystyle x=\frac{-b}{2a}}$ 
${\displaystyle =\frac{-(-10)}{2\times 0.25}}$ We changed a to 0.25 and b to -10.
${\displaystyle =\frac{10}{0.5}}$ We multiplied. 
${\displaystyle =20}$ We divided. 
There should be 20 fixtures produced each day.

Step 1
The total cost is given by:
$y=0.25x^2-10x+800$
Find the value of x that will give the minimum y.
Notice that the equation is that of a parabola that opens upward. So if you can find the vertex of this parabola, you will have found the minimum. The x-coordinate of the vertex of a parabola can be found by:
$x=\frac{-b}{2\times a}$ where the a and b come from:
$a{x}^2+bx+c=$
the general form for the quadratic equation.
In your problem, $a=0.25$ and $b=-10$
$x=\frac{-(-10)}{2\times (0.25)}$ Simplify.
$x=\frac{10}{0.5}$
$x=20$
So 20 fixtures should be produced each day to yield a minimum cost.
If you wanted to find this minimum cost, you would simply substitute x=20 into the original equation and solve for y.