Read a Quadratic Turning Point

A square makes a turning point

A quadratic is a polynomial of degree 2, with a nonzero squared-input coefficient and no higher-power terms. In a(x−h)²+k, the square is nonnegative and reaches zero at x=h. If a>0, all outputs are at least k, so the vertex (h,k) is a minimum. If a<0, all outputs are at most k, so it is a maximum. The vertex gives an ordered pair: h answers when or where the extremum occurs, while k answers how large its value is.