Question

in the equation f(x) = (x − h)^2 + k: what does k mean?

Answer 1

K would be the the y-coordinate of the vertex. It also determines the translation. If k is greater or less than zero, the function will translate up or down (up if K is positive and down if K is negative).

Answer 2

$\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} y=a(x-{{ h}})^2+{{ k}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})$

h = x-coordinate of the vertex point
k = y-coordinate of the vertex point