# What is the axis of symmetry and vertex for the graph y=-2x^2+5x-4?

Apr 17, 2018

See below

#### Explanation:

From the general quadratic $y = a {x}^{2} + b x + c$ the x coordinate of the vertex is given by $- \frac{b}{2 a}$

$\implies$ $- \frac{5}{2 \times - 2}$ =$\frac{5}{4}$

So the line of symmetry is $x = \frac{5}{4}$

To find the vertex, $y = - 2 \times {\left(\frac{5}{4}\right)}^{2} + 5 \times \frac{5}{4} - 4$

$\implies$ $y = - \frac{50}{16} + \frac{25}{4} - 4$ , $y = \frac{34}{16}$ $y = \frac{17}{8}$

The graph is an $n$ shaped parabola because it is a negative ${x}^{2}$, so the vertex is a maximum at $\left(\frac{5}{4} , \frac{17}{8}\right)$