Question

Can someone reword this?

Answer 1

The general equation of a parabola is" y = ax^2 + bx + c.
If "a" is positive, the parabola will be a vertical parabola that opens upward. Therefore it will have a u-shape and hence will have a minimum at the vertex.
If "a" is negative, the parabola will be a vertical parabola that opens downward. Therefore it will have an inverted u-shape and hence will have a maximum at the vertex.

In the example, x^2 - 6x + 8, "a" is +1 and so it will be a vertical parabola that opens upward and hence will have a minimum at the vertex.

The vertex can be found by completing the square.
Rewrite ax^2 + bx + c as a(x-h)^2 + k by completing the square. (h,k) will be the vertex.