rewrite an equation from standard to vertex form
(step by step)
[tex]y = {x}^{2} - 6x - 6[/tex]
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rewrite an equation from standard to vertex form
(step by step)
[tex]y = {x}^{2} - 6x - 6[/tex]
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To rewrite the equation from standard form to vertex form, follow these steps:
1. Start with the standard form equation:
\(y = x^2 - 6x - 6\)
2. Complete the square by adding and subtracting the square of half the coefficient of the x-term (\(-6/2 = -3\)):
\(y = x^2 - 6x + (-3)^2 - (-3)^2 - 6\)
3. Group the perfect square trinomial and constants:
\(y = (x^2 - 6x + 9) - 9 - 6\)
4. Simplify the perfect square trinomial and constants:
\(y = (x - 3)^2 - 15\)
So, the equation in vertex form is:
\(y = (x - 3)^2 - 15\)