This week in Pre Calc 11 we learned about equivalent forms of Quadratic Equations. Each Quadratic Function can be written in three different ways: Vertex Form, Factored Form and General Form and each form reveals different information that you may need to be able to graph a function.

A quadratic function in Vertex form tells us the scale factor and the coordinates of the vertex It looks like this:

A quadratic function in Factored form tells us the scale factor and the x-intercepts. It looks like this:

A quadratic function in General form tells us the scale factor the y-intercept and it also tells us if the parabola opens up or down. It looks like this:

We also learned how to find the vertex of a Quadratic function when it is in General Form. To do this you must first complete the square to solve for the vertex, because there are two variables in the function it will not be possible to solve completely, however it will give you the coordinates of the vertex in order to later graph it. Ex. In this example you must first get rid of the coefficient by dividing the first two terms by three. Ex. Then you must find the zero pairs by dividing the middle term by two and then squaring it. Ex.  Then you must simplify the first three terms and multiply the coefficient by to remove it from the brackets. Ex.  You are then able to combine like terms. Ex.  Once you have changed the equation into Vertex Form, you will be able to find the vertex needed to graph it. Vertex

If you wanted to find the x-intercepts, you would have to change the function from General Form to Factored Form by expanding the function and then factoring it.