f(x+1) = (x+1)^2 + 2(x+1) + 3.
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- + 2 + c = 6 \implies c = 3.
- Thus, the polynomial is \( f(x) = x^2 + 2x + 3 \).
- Now, calculate \( f(x+1) \):
- = x^2 + 2x + 1 + 2x + 2 + 3 = x^2 + 4x + 6.
- \(\boxed{x^2 + 4x + 6}\)
- Question: A retired engineer is helping design a new exhibit on conic sections. They explore the hyperbola given by \( 9x^2 - 16y^2 = 144 \). Determine the coordinates of its center.
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