# How do you tell whether the graph opens up or down, find the vertex, and find the axis of symmetry given #y=5x^2+1#?

##### 1 Answer

#### Explanation:

**Up or Down?** To tell whether a quadratic equation's graph opens up or down, look at whether the coefficient of x squared (number before x squared) is greater than or less than 0 (it can't be zero, cause then it isn't a quadratic equation). For example,

**Vertex?** If you are using this structure of quadratic equations (**x coordinate** of the vertex:

So you have x=0 for the vertex. To find the y coordinate, just plug in x=0 into the equation:

So now you have the coordinates for the vertex of

**Axis of Symmetry?** This is easy once you find the vertex. Because the vertex is sitting on the axis of symmetry, you just take the x value for up-down quadratic graphs (not sideways, that would be totally different) which, in this case, is ** #0#**, and set x to always =

#x=0#

A really helpful tool to have a visual guide is to use this graphing calculator, desmos.com/calculator where you can plug in any equation you want and have it graph it for you. Good luck on math!