Question

find the minimum value of the parabola \\(y = x^2\\).

simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Identify the vertex of the parabola

The given parabola is \(y = x^2\), which is in the standard vertex form \(y = a(x-h)^2 + k\) where \(a = 1\), \(h = 0\), and \(k = 0\). The vertex is at \((0, 0)\).

Determine the minimum value

Since the coefficient of \(x^2\) is \(a = 1 > 0\), the parabola opens upward. Therefore, the minimum value of the function occurs at the vertex, where \(y = 0\).

Answer:

Find the minimum value of the parabola \(y = x^2\).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

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