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Complete the square to rewrite y = x^2 - 6x + 14 In vertex form
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To rewrite the quadratic equation \( y = x^2 - 6x + 14 \) in vertex form, we will complete the square.
1. Start with the original equation:
\[
y = x^2 - 6x + 14
\]
2. Focus on the \( x^2 - 6x \) part. To complete the square, take the coefficient of \( x \) (which is \(-6\)), divide it by 2, and square it:
\[
\text{Half of } -6 = -3 \quad \text{and} \quad (-3)^2 = 9
\]
3. Add and subtract \( 9 \) inside the equation:
\[
y = (x^2 - 6x + 9) - 9 + 14
\]
4. Simplify the equation:
\[
y = (x - 3)^2 + 5
\]
Now, the equation \( y = x^2 - 6x + 14 \) in vertex form is:
\[
y = (x - 3)^2 + 5
\]
The vertex of the parabola is at the point \( (3, 5) \).
1. Start with the original equation:
\[
y = x^2 - 6x + 14
\]
2. Focus on the \( x^2 - 6x \) part. To complete the square, take the coefficient of \( x \) (which is \(-6\)), divide it by 2, and square it:
\[
\text{Half of } -6 = -3 \quad \text{and} \quad (-3)^2 = 9
\]
3. Add and subtract \( 9 \) inside the equation:
\[
y = (x^2 - 6x + 9) - 9 + 14
\]
4. Simplify the equation:
\[
y = (x - 3)^2 + 5
\]
Now, the equation \( y = x^2 - 6x + 14 \) in vertex form is:
\[
y = (x - 3)^2 + 5
\]
The vertex of the parabola is at the point \( (3, 5) \).
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