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Home » Why Every Kitchen Needs a Pantry-Stocked Ditch List: Canned Vegetables! - Abbey Badges

Why Every Kitchen Needs a Pantry-Stocked Ditch List: Canned Vegetables! - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Substitute \( (1, 0) \): \( 0 = a(1-2)^2 - 3 \).

📌 Simplifying, \( 0 = a(1) - 3 \), so \( a = 3 \).

📌 Expand to standard form: \( f(x) = 3(x-2)^2 - 3 = 3(x^2 - 4x + 4) - 3 = 3x^2 - 12x + 12 - 3 \).

📌 Thus, \( f(x) = 3x^2 - 12x + 9 \), so \( a = 3 \), \( b = -12 \), \( c = 9 \).

📌 #### \( a = 3, b = -12, c = 9 \)

📌 The sum of an infinite geometric series is 5, and the first term is 2. Find the common ratio.

📌 The sum \( S \) of an infinite geometric series is \( S = rac{a}{1-r} \).

📌 Given \( S = 5 \) and \( a = 2 \), we have \( rac{2}{1-r} = 5 \).

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\( x = rac{ -35 + \sqrt{1225 + 816} }{4} = rac{ -35 + \sqrt{2041} }{...
Since \( \sqrt{2041} pprox 45.18 \), \( x pprox rac{10.18}{4} ppro...
But for exactness, keep as:
The exact value is \( rac{ -35 + \sqrt{2041} }{4} \), but since width...
Final answer is \( oxed{rac{ -35 + \sqrt{2041} }{4}} \) â but this...
Alternatively, the problem may expect numerical, but in Olympiad, exac...
But let's assume it's solvable exactly:
Actually, mistake: 504 is not correct? Try \( x = 2 \): 24Ã19=456
\( x = 3 \): 26Ã21=546
- 456 = 48, 546 - 504 = 42, so not integer.

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