The direction a parabola opens is dependent on the coefficient of the x^2 term in its equation.
The equation of a parabola is generally expressed as y=ax^2 + bx + c. In this form, the coefficient 'a' determines the direction of the parabola. If 'a' is greater than 0, the parabola opens upwards. If 'a' is less than 0, the parabola opens downwards.
We have the equation of our parabola: y=(1/36)x^2 + (7/18)x - (23/36)
In this equation, the coefficient of the x^2 term is (1/36), which equals 0.027777777777777776. Since this value is greater than 0, we can conclude that the parabola opens upwards.
So, given the coefficient of x^2 in the equation of our parabola, we can confidently state that the parabola defined by the equation y=(1)/(36)x^(2)+(7)/(18)x-(23)/(36) opens upwards.