Determine the direction that this parabola opens y=x^2-6x

the graph of the parabola opens upwards.

Step-by-step explanation:

For any quadratic equation of the form

is true that:

if the main coefficient "a" is negative then the graph of the parabola opens downwards.

If the main coefficient "a" is positive, the parabola opens upwards

In this case the parabola is

Note that and therefore the graph of the parabola opens upwards.

We know that the number of workers doubles every week.

This implies that the number of workers of the previous week is exactly half of the current one's.

So, it took 11 weeks for the factory to be at half capacity.