Answer
Shift the parent function by $\frac{1}{2}$ unit to the left, vertically scale by a factor of 4, reflect across teh $x$-axis, shift by 13 units up
Work Step by Step
We are given the function:
$h(x)=-4x^2-4x+12$
Rewrite the function by completing the square:
$h(x)=-4(x^2+x)+12=-4\left(x+2\frac{1}{2}x+\dfrac{1}{4}\right)+4\left(\frac{1}{4}\right)+12=-4\left(x+\frac{1}{2}\right)^2+13$
We start graphing with the parent function $p(x)=x^2$.
First shift $p(x)$ by $\frac{1}{2}$ units to the left to get the function $g(x)=\left(x+\frac{1}{2}\right)^2$.
Then vertically scale $g(x)$ by a factor of 4 to get $k(x)=4\left(x+\frac{1}{2}\right)^2$.
Then reflect $k(x)$ across the $x$-axis to get the function $i(x)=-4\left(x+\frac{1}{2}\right)^2$.
Finally shift the function $i(x)$ by 13 units up to get the function $h(x)=-4\left(x+\frac{1}{2}\right)^2+13$.
Graph all transformations:
