7.
$$\mathrm { f } ( x ) = 2 x ^ { 2 } + 4 x + 9 \quad x \in \mathbb { R }$$
- Write \(\mathrm { f } ( x )\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are integers to be found.
- Sketch the curve with equation \(y = \mathrm { f } ( x )\) showing any points of intersection with the coordinate axes and the coordinates of any turning point.
- Describe fully the transformation that maps the curve with equation \(y = \mathrm { f } ( x )\) onto the curve with equation \(y = \mathrm { g } ( x )\) where
$$\mathrm { g } ( x ) = 2 ( x - 2 ) ^ { 2 } + 4 x - 3 \quad x \in \mathbb { R }$$
- Find the range of the function
$$\mathrm { h } ( x ) = \frac { 21 } { 2 x ^ { 2 } + 4 x + 9 } \quad x \in \mathbb { R }$$
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