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Home » \( \int -4x \, dx = -2x^2 \), - Dachbleche24

\( \int -4x \, dx = -2x^2 \), - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Dividing both sides by 3, \( w^2 = 64 \).

📌 Taking the square root, \( w = 8 \).

📌 A quadratic function \( f(x) = ax^2 + bx + c \) has roots at \( x = 2 \) and \( x = -3 \). If \( f(1) = 6 \), find the value of \( a \).

📌 Since the roots are 2 and -3, the function can be written as \( f(x) = a(x - 2)(x + 3) \).

📌 Expanding, \( f(x) = a(x^2 + x - 6) \).

📌 Substitute \( x = 1 \): \( f(1) = a(1^2 + 1 - 6) = a(-4) \).

📌 Given \( f(1) = 6 \), then \( -4a = 6 \).

📌 Solving, \( a = -\frac{3}{2} \).

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