h(x) is f(x) shifted 3 units left. So, \(h(x)=f(x+3)\)

Then stretched by a factor of 2. So \(h(x)= 2f(x+3)\)

Reflected accross x axis. So, \(h(x) = -2f(x+3)\)

Then shifted up 7. \(h(x)= -2f(x+3)+7= -2(x+3)^2 + 7\)

Answer: \(h(x) = -2(x+3)^2 + 7\)

We compare h(x) with \(a(x-h)^2+k\). So \(h=-3\) and \(k=7\).

Vertex\(=(h,k)=(-3,7)\)

Answer:Vertex\(= (-3,7)\)

\(h(x)=-2(x+3)^2+7\)