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Find the vertex of the graph of the equation $x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14$.

 Nov 18, 2023
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We can rewrite the equation as \begin{align*} x -y^2 + 8y &= 13 + 2y + y^2 - 7y - 14\ 2y^2 + 9y + x &= 0\ 2(y^2 + \tfrac{9}{2}y + \tfrac{x}{2}) &= 0 \ 0 &= (y+\tfrac{9}{4})^2 + x - \tfrac{81}{16} \end{align*}This is a parabola, opening upwards, with vertex at (1681​,4−9​).

 Nov 18, 2023

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