What is the vertex of  y= -x^2 +9x - 8?

Jul 26, 2017

Vertex: $\left(\frac{9}{2} , \frac{49}{4}\right)$

Explanation:

Apply the vertex formula: $x = - \frac{b}{2 a}$, where $a = - 1$ and $b = 9$

Thus,

$x = - \frac{9}{2 \left(- 1\right)}$

$x = \frac{9}{2}$

We must now find the $y$-value for the vertex which we can find by substituting $\frac{9}{2}$ for $x$ in the given equation $y = - {x}^{2} + 9 x - 8$. So...

$- {\left(\frac{9}{2}\right)}^{2} + 9 \left(\frac{9}{2}\right) - 8$

$y = - \frac{81}{4} + \frac{81}{2} - 8$

Find the LCD of $4 , 2$ and $1$; that is $4$

$y = - \frac{81}{4} + \frac{81 \times 2}{2 \times 2} - \frac{8 \times 4}{1 \times 4}$

$y = - \frac{81}{4} + \frac{162}{4} - \frac{32}{4}$

$y = \frac{- 81 + 162 - 32}{4}$

$y = \frac{49}{4}$

And so the vertex is $\left(\frac{9}{2} , \frac{49}{4}\right)$