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

##### 1 Answer

The graph (the Parabola) Opens Up, as the coefficient of

Vertex

#### Explanation:

Standard Form of a Quadratic Equation is given by

If

Since in our Quadratic Equation, the coefficient of the

Also observe that, if the Parabola "Opens Upward" then our Vertex will be a "Minimum" of the Quadratic Function.

We are given the Quadratic Function

The expression

To obtain the y-coordinate value of the "Vertex", substitute the value obtained from using the expression

Hence,

After simplification, we get

Hence our Vertex

And our Axis of Symmetry

Please refer to the attached graph for a visual proof of our solution.

I hope this explanation is helpful.