The General Form and Standard Form can be converted to Equivalent Forms. This can be useful if you are trying to find the vertex or y-intercept.

To convert from General Form to Standard Form we complete the square:

Now we know that the vertex is at (-3, -3)

To convert from Standard Form to General Form we expand the equation:

Now we know that the y-intercept is at 15.

This week in Math I learned about the General and Standard forms of the Quadratic Function and how to analyze them. Both General Form and Standard Form equations make parabolas. You can identify many characteristics of a parabola just by looking at a Standard Form or General Form Quadratic Function.

General Form look like this:

In the General Form C always tells you the y-intercept. A tells you if the parabola opens up or down (if it is negative the parabola opens down if it is positive the parabola opens up). A also tells you if the parabola stretches or compresses (if a is bigger than 1 the parabola stretches if a is smaller than 1 the parabola compresses). A cannot be 0.

Standard Form looks like this:

In General Form q tells you the vertical translation or the y-axis of the vertex (q is not always the y-int). P tells you the horizontal translation or the x-axis of the vertex. Using p and q you can identify the vertex of a parabola. A tells you if the parabola opens up or down (if it is negative the parabola opens down if it is positive the parabola opens up). A also tells you if the parabola stretches or compresses (if a is bigger than 1 the parabola stretches if a is smaller than 1 the parabola compresses). A cannot be 0.