Answer
(a) $h$, $k$
(b) $\text{upward}; \text{minimum}$
(c) $\text{downward}; \text{maximum}$
Work Step by Step
RECALL:
(1) Th graph of a quadratic function is a parabola.
(2) The standard form of a quadratic function is $f(x) = a(x-h)^2+k$ where $(h, k)$ is the vertex. The graph opens upward when $a \gt 0$ and opens downward when $a \lt 0$.
(3) The quadratic function $f(x) = (x-h)^2+k$ has $k$ as its
(i) minimum when $a\gt0$; and
(ii) maximum when $a \lt 0$
Thus, the missing expression in the given statements are:
(a) $h$, $k$
(b) $\text{upward}; \text{minimum}$
(c) $\text{downward}; \text{maximum}$
