A restricted downward parabola

8 written marks

Let \(h(x)=-2x^2+12x-9\), with domain \(0\le x\le4\).

1. Write \(h(x)\) in completed-square form.

   [3]

2. Find the range of \(h\) on this domain.

   [2]

3. Find all real \(t\) for which \(h(x)=t\) has exactly one solution in \([0,4]\).

   [3]

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