legend of vox machina - Sourci

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📰 Solution: The standard form of a parabola with vertical axis is $ y = \frac{1}{4p}x^2 $. The focus is at $ (0, p) $, so $ p = 5 $. The width of 20 units implies the parabola passes through $ (10, 5) $. Substituting: $ 5 = \frac{1}{20}(100) \Rightarrow 5 = 5 $, which holds. Thus, the equation is $ y = \frac{1}{20}x^2 $. \boxed{y = \dfrac{1}{20}x^2} 📰 Question: An ichthyologist models fish population growth with a quadratic function $ h(x) $ satisfying $ h(1) = 4 $, $ h(2) = 11 $, and $ h(3) = 22 $. Find $ h(4) $. 📰 Solution: Assume $ h(x) = ax^2 + bx + c $. Using $ h(1) = a + b + c = 4 $, $ h(2) = 4a + 2b + c = 11 $, $ h(3) = 9a + 3b + c = 22 $. Subtract first equation from second: $ 3a + b = 7 $. Subtract second from third: $ 5a + b = 11 $. Subtract these: $ 2a = 4 \Rightarrow a = 2 $. Then $ 3(2) + b = 7 \Rightarrow b = 1 $. From $ 2 + 1 + c = 4 \Rightarrow c = 1 $. Thus, $ h(x) = 2x^2 + x + 1 $, and $ h(4) = 32 + 4 + 1 = 37 $. \boxed{37} 📰 Debit Card Processing 📰 Viral News Why Isn T My Fortnite Working And The World Reacts 📰 Javascript Reduce 📰 Fha Loan Lenders 📰 Christmas Dad Jokes You Didnt Know You Neededrelatable Kid Friendly And Totally Funny 3359468 📰 Oblivion Game Cheats 📰 You Wont Believe What This Vag Typeface Can Transform Your Brands Personality 5981002 📰 Police Reveal Theory Of Red String And It Leaves Everyone Stunned 📰 Microsoft Modern Wireless Headset 📰 Small Business Credit Card 1141876 📰 Elemental Dungeon 📰 4 From Lullabies To Lifelong Loyalty How Ohana Means Family Shapes Generations 2380550 📰 What Is A Wooden Nickel 📰 Home Interest Rates Us Bank 7862315 📰 Dynamics 365 Operations And Finance