Answer
(a) Parent function: $f(x)=x^2$
(b) A translation of $2$ units left, reflection across the $x$-axis and translation of $3$ units up.
(c) The graph of $h$ is as shown.
(d) $h(x)=-f(x+2)+3$
Work Step by Step
(a) Parent function:
$$f(x)=x^2$$
(b) The transformation is a translation of $2$ units left, reflection across the $x$-axis and translation of $3$ units up.
(c) The graph of $h$ is as shown.
(d) $h$ in terms of $f$:
$$h(x)=-f(x+2)+3$$
