Find the largest and smallest value of the function y = 3x ^ 2 – 6 on the segment [0; 3]

On the segment [0; 3], a function is given, more precisely, an incomplete trinomial y = y (x) = 3 * x ^ 2 – 6, for which you need to determine the largest and smallest values.
As you know, the graph of the trinomial y = a * x ^ 2 + b * x + c is a parabola. The axis of the parabola y = a * x ^ 2 + b * x + c is the straight line x = (–b) / (2 * a). The ordinate of the vertex of the parabola is calculated by the formula y0 = y (x0).
For the considered trinomial y = 3 * x ^ 2 – 6, we have a = 3, b = 0 and c = –6. Therefore, the abscissa x0 of the vertex of the parabola is equal to x0 = 0 / (2 * 3) = 0. Now we find y0 = 3 * x ^ 2 – 6 = 3 * 0 – 6 = –6. So, (0; –6) is the vertex of the parabola y = 3 * x ^ 2 – 6. Since, a = 3> 0, the branches of the parabola are directed upwards, therefore, the function y = 3 * x2 – 6 at the point x = 0 takes the smallest value y0 = –6.
It remains to calculate the value of the function y = 3 * x ^ 2 – 6 at the point x1 = 3. We have y (x1) = 3 * 3 ^ 2 – 6 = 3 * 9 – 6 = 27 – 6 = 21. This is the largest value functions y = 3 * x ^ 2 – 6 on the segment [0; 3].
Answer: 21; –6.