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📰 5Question: Find the quadratic polynomial $ h(x) $ such that $ h(1) = 5 $, $ h(-1) = 3 $, and the sum of its roots is $ 4 $. 📰 Solution: Let $ h(x) = ax^2 + bx + c $. From $ h(1) = a + b + c = 5 $ and $ h(-1) = a - b + c = 3 $, adding gives $ 2a + 2c = 8 $, so $ a + c = 4 $. The sum of roots is $ -rac{b}{a} = 4 $, so $ b = -4a $. Substituting $ b = -4a $ into $ a + b + c = 5 $: $ a - 4a + c = 5 $ → $ -3a + c = 5 $. Since $ a + c = 4 $, subtracting gives $ -4a = 1 $, so $ a = -rac{1}{4} $. Then $ c = 4 - a = 4 + rac{1}{4} = rac{17}{4} $, and $ b = -4a = 1 $. Thus, $ h(x) = -rac{1}{4}x^2 + x + rac{17}{4} $. Multiplying by 4 to eliminate fractions: $ h(x) = -x^2 + 4x + 17 $. Verifying $ h(1) = -1 + 4 + 17 = 20 $? Wait, inconsistency. Rechecking: $ a = -1/4 $, $ c = 17/4 $, $ b = 1 $. Then $ h(1) = -1/4 + 1 + 17/4 = (-1 + 4 + 17)/4 = 20/4 = 5 $, correct. $ h(-1) = -1/4 -1 + 17/4 = ( -1 -4 + 17 )/4 = 12/4 = 3 $, correct. Sum of roots $ -b/a = -1 / (-1/4) = 4 $, correct. Final answer: $ oxed{-x^2 + 4x + \dfrac{17}{4}} $ or $ oxed{-\dfrac{1}{4}x^2 + x + \dfrac{17}{4}} $. 📰 Question: A science communicator observes that the number of views $ V(t) $ on a video grows quadratically over time $ t $ (in days). If $ V(1) = 120 $, $ V(2) = 200 $, and $ V(3) = 300 $, find $ V(4) $. 📰 Inside The Shocking Truth About Wrenches That Break Tasks 1033809 📰 You Wont Believe The One Simple Hack To Reheat Rice Like A Pro 4658606 📰 God Vishnu Sahasranamam 5870786 📰 The Sequence Described Is Similar To The Fibonacci Sequence Starting With F1 1 And F2 1 The Terms Are Calculated As Follows 9377071 📰 Credit Card Merchant Fee 3311377 📰 Billy Baker 4570356 📰 Maximal Combat Is Real Mortal Kombat Xl Unleashed Watch The Legends Clash 1615440 📰 Zeas Menu 9670378 📰 Mozilla Download Page 3494475 📰 May Carilion Clinic Be Keeping The Secret Thats Ruining Lives 1700940 📰 Finally Revealed The Powerful Outlook Signature You Need To Stand Out 8670467 📰 None Will Suspect It Secret Turkey Disguise Ideas Guaranteed To Blend In 9465136 📰 Cant Find Your Ms Serial Number Click Here To Locate It Instantly 9148744 📰 Youll Never Believe How One Simple Hole Transformed Gaming Forever 5714919 📰 Dont Miss The Next Bus Wash In Washington Dcget Verdenty Clean Every Ride 4924077