To complete the square for the quadratic equation \( y = x^2 - 16x + 14 \), follow these steps:
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Start with the equation: \[ y = x^2 - 16x + 14 \]
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To complete the square, focus on the \( x^2 - 16x \) part. Take half of the coefficient of \( x \) (which is -16), square it, and add it inside the equation: \[ \text{Half of } -16 = -8 \] \[ \text{Square it: } (-8)^2 = 64 \]
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Add and subtract this square inside the equation: \[ y = (x^2 - 16x + 64) - 64 + 14 \]
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Rewrite the equation by factoring the perfect square trinomial and simplifying: \[ y = (x - 8)^2 - 50 \]
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Now, we can identify the vertex of the parabola. The vertex form of a quadratic equation is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex. From our equation: \[ (h, k) = (8, -50) \]
Thus, the vertex of the quadratic equation \( y = x^2 - 16x + 14 \) is at the point \( (8, -50) \).
The correct answer is: a (8, -50).
1 answer