Does the parabola y = -3x^2 + 2x - 1 have a maximum or minimum value?

(1) Find out if it has a Stationary Point.

Take the derivative of y.
Solve for x when the derivative is 0.

(2) If it does, determine their status as maxima, minima, or inflection(s).

Inspect the values of the curve slightly before and after the point(s).

To determine whether the parabola y = -3x^2 + 2x - 1 has a maximum or minimum value, we can look at the coefficient of the x^2 term. If the coefficient is positive, the parabola opens upward, meaning it has a minimum value. Conversely, if the coefficient is negative, the parabola opens downward, indicating it has a maximum value.

In this case, we have -3x^2 as the coefficient of the x^2 term, which is negative. Therefore, the parabola y = -3x^2 + 2x - 1 has a maximum value.