Answer
(a) Parent function: $f(x)=x^2$
(b) A vertical compression of a factor of $2$, translation of $1$ unit right, reflection across the $x$-axis and translation of $2$ units down.
(c) The graph of $h$ is as shown.
(d) $h(x)=\frac{1}{2}f(x-1)-2$
Work Step by Step
(a) Parent function:
$$f(x)=x^2$$
(b) The transformation is a vertical compression of a factor of $2$, translation of $1$ unit right, reflection across the $x$-axis and translation of $2$ units down.
(c) The graph of $h$ is as shown.
(d) $h$ in terms of $f$ is:
$$h(x)=\frac{1}{2}f(x-1)-2$$
