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Home » Find the derivative of \( f(x) = 3x^2 + 5x - 7 \). - Sterling Industries

Find the derivative of \( f(x) = 3x^2 + 5x - 7 \). - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 We have \( xy = 56 \) and \( x + y = 15 \).

📌 Solving the quadratic \( t^2 - 15t + 56 = 0 \) using the quadratic formula:

📌 t = rac{15 \pm \sqrt{15^2 - 4 imes 56}}{2} = rac{15 \pm \sqrt{225 - 224}}{2} = rac{15 \pm 1}{2}

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

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