Suggestion

The graph of the function \[y=2^{x^2-4x+3}\] can be obtained from the graph of \(y = 2^{x^2}\) by

  1. a stretch parallel to the \(y\)-axis followed by a translation parallel to the \(y\)-axis.
  2. a translation parallel to the \(x\)-axis followed by a stretch parallel to the \(y\)-axis.
  3. a translation parallel to the \(x\)-axis followed by one parallel to the \(x\)-axis.
  4. a translation parallel to the \(x\)-axis followed by a reflection in the \(y\)-axis.
  5. a reflection parallel to the \(y\)-axis followed by a translation parallel to the \(y\)-axis.

The starting and finishing functions differ by \(x^2 \mapsto x^2-4x+3\). Could we rewrite the latter to look like a transformation?