To complete the square for the quadratic equation \( y = x^2 - 16x + 14 \), we proceed as follows:
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Start with the quadratic terms: \[ y = x^2 - 16x + 14 \]
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We need to complete the square for the expression \( x^2 - 16x \). To do this, take half of the coefficient of \( x \) (which is \(-16\)), square it, and add/subtract that term inside the equation.
- Half of \(-16\) is \(-8\).
- Squaring it gives \((-8)^2 = 64\).
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Rewrite the equation by adding and subtracting \( 64 \): \[ y = (x^2 - 16x + 64) - 64 + 14 \]
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This simplifies to: \[ y = (x - 8)^2 - 50 \]
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Now, the equation is in vertex form \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. Here, \( h = 8 \) and \( k = -50 \).
Thus, the vertex of the parabola is \((8, -50)\).
The answer is: C. (8, -50).
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