# What is the vertex and focus of the parabola described by x^2-4x+y+3=0?

May 12, 2017

${x}^{2} - 4 x + y + 3 = 0$
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$y = - {x}^{2} + 4 x - 3$
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$y = - \left({x}^{2} - 4 x + 3\right)$
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$y = - \left({x}^{2} - 4 x + 3 + 1 - 1\right)$
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$y = - \left({x}^{2} - 4 x + 4 - 1\right)$
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$y = - \left({x}^{2} - 4 x + 4\right) + 1$
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$y = - {\left(x - 2\right)}^{2} + 1$
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The vertex of the parabola is $\left(2 , 1\right)$
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The focus of thus parabola is $- \frac{1}{4}$