9 Fig. 9 shows the curves \(y = \frac { 1 } { x + 2 }\) and \(y = x ^ { 2 } + 7 x + 7\).
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\includegraphics[alt={},max width=\textwidth]{2ebf7ad2-638f-4378-b98d-aadd0de4c766-3_1255_1470_434_299}
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\caption{Fig. 9}
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- Use Fig. 9 to estimate graphically the roots of the equation \(\frac { 1 } { x + 2 } = x ^ { 2 } + 7 x + 7\).
- Show that the equation in part (i) may be simplified to \(x ^ { 3 } + 9 x ^ { 2 } + 21 x + 13 = 0\). Find algebraically the exact roots of this equation.
- The curve \(y = x ^ { 2 } + 7 x + 7\) is translated by \(\binom { 3 } { 0 }\).
(A) Show graphically that the translated curve intersects the curve \(y = \frac { 1 } { x + 2 }\) at only one point. Estimate the coordinates of this point.
(B) Find the equation of the translated curve, simplifying your answer.