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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 In a development project, a quadratic function \( h(x) = x^2 - 4x + c \) models the height of a support beam, where \( c \) is a constant. Determine \( c \) such that the function has exactly one real root.

📌 For a quadratic equation \( ax^2 + bx + c = 0 \) to have exactly one real root, its discriminant must be zero. The discriminant \(\Delta\) is given by:

📌 \Delta = b^2 - 4ac

📌 For the function \( h(x) = x^2 - 4x + c \), we have \( a = 1 \), \( b = -4 \), and \( c = c \). Set the discriminant to zero:

📌 Solve for \( c \):

📌 4c = 16 \quad \Rightarrow \quad c = 4

📌 Thus, the value of \( c \) is \(\boxed{4}\).

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