Order the group of quadratic functions from widest to narrowest graph y = - 7x ^ 2, y = - 1/5 x ^ 2, y = - 1/3 * x ^ 2
1) y = - 1/5 * x ^ 2, y = - 7x ^ 2 , 2) y = - 1/3 * x ^ 2;
3) y = - 1/5 * x ^ 2, y = - 1/3 * x ^ 4) 2, y = - 7x ^ 2;
5) y = - 7x ^ 2; y = - 1/3 * x ^ 2, y = - 1/5 * x ^ 2

His profit in dollars per day is 91.

Step-by-step explanation:

You know that the net profit in dollars per day for a small business owner is given by the equation f(x) = -0.1*x² + 6*x + 1, where x is the number of employees he hires.

If he hires the number of employees that will maximize his profit, then this indicates that I should look for the maximum of the function f (x).

A quadratic function or second degree function is a polynomial function defined as:

f(x)= a*x² + b*x + c

If the scalar a> 0, the parabola opens upwards and the vertex is the minimum of the function. On the other hand, if a <0, the parabola opens downwards and the vertex is the maximum of the function.

In this case, having a value of -0.1, the vertex will indicate the maximum of the function.

The maximum in x is then reached when:

In this case, being a=-0.1 and b=6, you get:

The number of employees who will maximize their profits is 30. So, replacing in the function f (x) you get:

f(30) = -0.1*30² + 6*30 + 1

Solving:

f(30)= 91

His profit in dollars per day is 91.