Our parabola open downward and therefore a is negative.
Explanation: As value of a changes from positive to negative or from negative to positive, the direction of opening changes. For negative values of a we got negative parabolas that open downward. As the original formula y = x^2 we see that x^2 will always be positive because when you square a number it always gives positive value. Therefore the direction for which it will open, depends on value of a.
If the x is squared or if a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left. The vertex is at (h, k).
