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📰 Solution: Assume $ f $ is quadratic: $ f(x) = ax^2 + bx + c $. Substitute into the equation: $ a(x + y)^2 + b(x + y) + c = ax^2 + bx + c + ay^2 + by + c + 2xy $. Expand and compare coefficients: $ ax^2 + 2axy + ay^2 + bx + by + c = ax^2 + ay^2 + bx + by + 2c + 2xy $. Matching terms: $ 2a = 2 \Rightarrow a = 1 $, and $ 2c = c \Rightarrow c = 0 $. Thus, $ f(x) = x^2 + bx $. Any real $ b $ satisfies the equation, so there are infinitely many solutions. Final answer: $oxed{\infty}$ 📰 Question: Find the center of the hyperbola $ 9x^2 - 18x - 16y^2 - 64y = 144 $. 📰 Solution: Group terms: $ 9(x^2 - 2x) - 16(y^2 + 4y) = 144 $. Complete the square: $ 9[(x - 1)^2 - 1] - 16[(y + 2)^2 - 4] = 144 $. Expand: $ 9(x - 1)^2 - 9 - 16(y + 2)^2 + 64 = 144 $. Simplify: $ 9(x - 1)^2 - 16(y + 2)^2 = 89 $. The center is at $ (1, -2) $. Final answer: $oxed 📰 Survive The Natural Disasters 2544493 📰 Hyatt Regency Savannah Ga 8787113 📰 Watch These Farva Super Troopers Dominate In Ways No One Expected 4015330 📰 Windows 7 License Key Activation 6012749 📰 Charlie Kirks Staggering Net Worth Revealed By Forbesx Millions You Wont Believe How He Built It 189676 📰 Lock In The Most Elegant Waylicense Plate Frames That Steal The Spotlight 2949129 📰 How Many Grammys Has Beyonce Won 3520030 📰 Your Job Could Be At Risk At West Penn Hospitalheres Whats Really Happening 5932423 📰 Aaron Pierre Girlfriend 1871243 📰 Why All Watercolor Paper Is A Liethis Is The Real Difference 8976851 📰 Alan Wake 2 Download 5821372 📰 Woody Harrelson Net Worth 50M The Truth Behind His Hollywood Fortuneelemental 3478621 📰 Orlando Vacation Packages 2053742 📰 Free Software Pdf Merge 8563791 📰 Zodiac Sign For Sep 23 8676598