## Find the parabola's parts and create vertical parabola.

For example, the equation y = 2(*x* – 1)^{2} – 3, has its vertex at (1, –3). This means that *a* = 2, *h* = 1, and *v* = –3. With this information, you can identify all the parts of a parabola (axis of symmetry, focus, and directrix) as points or equations:

First, find the axis of symmetry. The axis of symmetry is at *x* = *h*, which means that *x* = 1.

Second, determine the focal distance and write the focus as a point. You can find the focal distance by using the formula 1/(4*a*). Because *a* = 2, the focal distance for this parabola is 1/8. With this distance, you can write the focus as the point (*h*,*v* + 1/4*a*), or (1,–2-7/8)

Third, find the directrix. You can use the equation of the directrix: *y* = *v* – 1/4*a*, or *y* = –3-1/8.

Last, graph the parabola and label all its parts as shown.

It is always a good idea to plot at least two other points besides the vertex so that you can show that your vertical transformation is correct. Because the vertical transformation in this equation is a factor of 2, the two points on both sides of the vertex will be stretched by a factor of two.

So, from the vertex, you plot a point that is to the right one, and up two (instead of up one). Then you can draw the same point on the other side of the axis of symmetry; the two other points on the graph are at (2, –1) and (0, –1).