Problem

Find the perfect square trinomial for the quadratic equation \(y = x^2 + 4x + c\), and determine the value of \(c\).

Answer

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Answer

Step 3: Substitute \(b = 2\) into \(b^2 = c\) to find \(c\). This simplifies to \(c = 2^2\), which simplifies to \(c = 4\).

Steps

Step 1 ：Step 1: The formula for a perfect square trinomial is \(a^2 + 2ab + b^2\). Comparing this with the given equation \(y = x^2 + 4x + c\), we see that \(a = x\), \(2ab = 4x\), and \(b^2 = c\).

Step 2 ：Step 2: From \(2ab = 4x\), we can derive that \(2*x*b = 4x\), which simplifies to \(b = 2\).

Step 3 ：Step 3: Substitute \(b = 2\) into \(b^2 = c\) to find \(c\). This simplifies to \(c = 2^2\), which simplifies to \(c = 4\).

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