Parabola
When we graphed y = x 2 we got a shape that kind of looks like the letter U in print or the shape of a wine glass. This is a very special shape called a PARABOLA .
Any time you graph something with an x 2 in it, you will get some variation of a parabola.
Any function with an x 2 in it is called a quadratic function .
In real life, besides a wine glass, or the letter U, the shape of a parabola can be found in some objects and situations.
For example:
The path that a kicked soccer ball takes as it travels through the air.
A jet of water spouting out of a fountain.
Some bridges.
The inside of a satellite dish.
The lowest point ( minimum value ) of the graph y = x 2 sits on the origin (0, 0). This is called the VERTEX .
We will learn that the parabola can be flipped upside down. In this case the vertex would be the maximum value (like the very top of a hill).
A parabola is a perfect mirror image (the left side and the right side are exactly the same). If we were to draw a line right down the middle and through the vertex, this is called the axis of symmetry .
When we plot y = x 2 , the axis of symmetry is actually the same line as the y axis.

Parabola opens down.
Vertex is a maximum value at
(0, 0)
Axis of symmetry
Vertex
Parabola opens upward.
Vertex is a minimum value at
(0,0)
Vertex
Axis of symmetry