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Greetings. I found the X in the vertices applying the -b/2a and getting -1/4, however, when I try to solve for y I get -75/8 or -9 3/8 (I even placed the equation in WolframAlpha and got the same answer. What am I doing wrong?

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    $\begingroup$ I get this as well. $\endgroup$ Mar 18 at 14:33
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    $\begingroup$ Did you try to enter the solution as $-{75\over8}$? $\endgroup$ Mar 18 at 14:36
  • $\begingroup$ @Intelligentipauca Yes, I found out that I had to input the answering a fraction. Thank you $\endgroup$
    – יהודה
    Mar 18 at 19:37

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$\begin{equation} \begin{split} y &= 6 x^2 + 3 x - 9 \\ &= 6 (x^2 + \frac{1}{2} x) - 9 \\ &= 6 ( (x + \frac{1}{4} )^2 - \frac{1}{16} ) - 9 \\ & = 6 (x + \frac{1}{4})^2 - \frac{3}{8} - 9 \\ &= 6 (x + \frac{1}{4})^2 - \frac{75}{8} \\ \end{split}\end{equation}$

Which means the vertex is at $(-\dfrac{1}{4}, - \dfrac{75}{8} ) $

So your answer is correct.

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