How to find the coordinates of the vertex of the 2x parabola in the –5x + 8 square?

From the function y = (2 x ^ 2 – 5 x + 8), select the square:

y = 2 * (x ^ 2 – 5x / 2 + 4),

farther:

y = 2 * ((x – 5/4) ^ 2 – 25/16 + 4);

y = 2 * ((x – 5/4) ^ 2 – 25/16 + 64/16);

y = 2 * ((x – 5/4) ^ 2 + 39/16).

Thus, the vertex of the parabola is located at the point with the coordinate x = 5/4 and, accordingly, y = 2 * 39/16 = 39/8 = 4.875.

For any other value of x, the value of the function y will be greater than 4.875.

Answer: the vertex is at a point with coordinates: x = 5/4; y = 39/8 = 4.875.