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Home » $U_8 = T_7 = 24$ - Groen Casting

$U_8 = T_7 = 24$ - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The solutions are \( t = 8 \) and \( t = 7 \).

📌 A function \( f(x) = ax^2 + bx + c \) has a vertex at \( (2, -3) \) and passes through the point \( (1, 0) \). Find \( a \), \( b \), and \( c \).

📌 The vertex form is \( f(x) = a(x-2)^2 - 3 \).

📌 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 \( a = 3 \), \( b = -12 \), \( c = 9 \).

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