Question

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

Answer 1

See below

Explanation:

From the general quadratic `y=ax^2+bx +c` the x coordinate of the vertex is given by `-b/(2a)`

`=>` `-5/(2xx-2)` =`5/4`

So the line of symmetry is `x=5/4`

To find the vertex, `y=-2xx(5/4)^2+5xx5/4-4`

`=>` `y=-50/(16)+25/4-4` , `y=34/(16)` `y=17/8`

The graph is an `n` shaped parabola because it is a negative `x^2`, so the vertex is a maximum at `(5/4,17/8)`