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#?
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 (
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
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!