# How do you tell whether the graph opens up or down, find the vertex, and find the axis of symmetry given #y=1/10x^2+x-2#?

##### 1 Answer

The graph 'opens upwards'.

Vertex

Axis of symmetry

#### Explanation:

If the coefficient of

is positive then the graph is of form

If the coefficient of

In this case the coefficient is

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are several ways but I am going to show you a shortcut. The method forms part of the process for 'completing the square.

Consider the standardised form of

Write as

Note that

We have the equation:

Where

Substitute for

Vertex

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This is a line that is parallel to the y-axis and passes through

So axis of symmetry is