# How do you find the axis of symmetry and vertex point of the function:  y = -x^2 + 3x + 5?

Oct 18, 2015

Vertex $\left(\frac{3}{2} , \frac{29}{4}\right)$

Axis of Symmetry $x = \frac{3}{2}$

#### Explanation:

Given -

$y = - {x}^{2} + 3 x + 5$

Vertex point -

$x = \frac{- b}{2 a} = \frac{- 3}{2 \times \left(- 1\right)} = \frac{- 3}{- 2} = \frac{3}{2}$

$y = - {\left(\frac{3}{2}\right)}^{2} + 3 \left(\frac{3}{2}\right) + 5$

$y = \frac{- 9 + 18 + 20}{4} = \frac{29}{4}$

Vertex $\left(\frac{3}{2} , \frac{29}{4}\right)$

Axis of Symmetry $x = \frac{3}{2}$