When graphing a quadratic equation, the resulting shape is not a straight line, but instead a shape called a parabola. Parabolas vary in direction and shape. The lowest or highest point in a parabola is called a vertex, which lies on the axis of symmetry. If the leading coefficient of the term to the second degree is positive, the parabola faces up. If it is negative, the parabola faces down.
The graph of y equals x squared is, as you know, called a parabola, okay? And, basically, what I'm going to do now is just give you some language that goes along with that.
The lowest point is called the vertex. It could also be the highest point if the parabola is facing the other direction.
And there is also what's called the axis of symmetry, which is basically an invisible line that goes down the center of the graph. So if you folded it over, it would actually be symmetric about that line, okay?
Depending on your teacher or whatnot, you are going to have to do various levels of precision, okay? Some teachers just want to see a vertex in the general shape. Other teachers want to see specific points, sometimes three, sometimes five. So what you need to do is find a point here and point here.
The cool thing about the axis of symmetry is if you find a point on the right side of your graph, you can always just transpose it over to the other side. If you are out two units and up, say, two units, you know that then you are out two and up two. If you are out three and up five, you also know that you are out three and up five on the other side.
Using the axis of symmetry could be really helpful in taking shortcuts in finding points in order to plot your graph.
Basically the main association we are going to talk about right now is your vertex and your axis of symmetry.