let's put h(x) in vertex form, and then let's see if we can get f(x) from there.
![~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{vertex}{\stackrel{h}{0}~~,~~\stackrel{k}{-3}}\qquad h(x)=a(x-0)^2-3 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cstackrel%7Bvertex%7D%7B%5Cstackrel%7Bh%7D%7B0%7D~~%2C~~%5Cstackrel%7Bk%7D%7B-3%7D%7D%5Cqquad%20h%28x%29%3Da%28x-0%29%5E2-3%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![h(x+2)=a[(x+2)-0]^2-3\implies h(x+2)=\underline{a(x+2)^2-3} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \underline{h(x+2)}-5\implies [a(x+2)^2-3]~~ - ~~5\implies &\boxed{a(x+2)^2-8=f(x)} \\\\ &a[x-\stackrel{h}{(-2)}]^2\stackrel{k}{-8}=f(x)\\\\ &\stackrel{vertex}{-2~~,~~-8} \end{array}](https://tex.z-dn.net/?f=h%28x%2B2%29%3Da%5B%28x%2B2%29-0%5D%5E2-3%5Cimplies%20h%28x%2B2%29%3D%5Cunderline%7Ba%28x%2B2%29%5E2-3%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Cunderline%7Bh%28x%2B2%29%7D-5%5Cimplies%20%5Ba%28x%2B2%29%5E2-3%5D~~%20-%20~~5%5Cimplies%20%26%5Cboxed%7Ba%28x%2B2%29%5E2-8%3Df%28x%29%7D%20%5C%5C%5C%5C%20%26a%5Bx-%5Cstackrel%7Bh%7D%7B%28-2%29%7D%5D%5E2%5Cstackrel%7Bk%7D%7B-8%7D%3Df%28x%29%5C%5C%5C%5C%20%26%5Cstackrel%7Bvertex%7D%7B-2~~%2C~~-8%7D%20%5Cend%7Barray%7D)
You move the decimal point forward until it reaches the one so it looks like this:
1.4 x 10⁵
the exponent, 5, just tells you how many spaces the decimal point moved.
The cube root of 343 is 7.
One side has an area of 7*7 = 49 square cm
There are 6 sides to a cube
6 * 49 is the surface area = 294