# What is the vertex form of y=9x^2 - 17x - 85 ?

Jun 8, 2017

For the method in detail have a look at:
https://socratic.org/s/aFpc6GYR

$y = 9 {\left(x - \frac{17}{18}\right)}^{2} - \frac{3349}{36}$

#### Explanation:

$y = 9 {\left(x - \frac{17}{2 \times 9}\right)}^{2} + k - 85$

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Note that $\text{ } 9 {\left(- \frac{17}{2 \times 9}\right)}^{2} + k = 0$

$\implies {17}^{2} / 36 + k = 0$

$\implies k = - \frac{289}{36} = - 8 \frac{1}{36}$
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$y = 9 {\left(x - \frac{17}{2 \times 9}\right)}^{2} - 8 \frac{1}{36} - 85$

$y = 9 {\left(x - \frac{17}{18}\right)}^{2} - \frac{3349}{36}$