This week in Precal we learned about the three forms of quadratic functions in which there’s the vertex/general form, standard form and, factored form. We learned on how to convert from one form to another to get enough information in order to graph an equation such as the vertex, the intercepts, the translations and so on.

First of, we learned what the letters in the vertex form (aside from the x and y letters) are and how they affect the whole equation when it’s being graph:

+ q = y

starting off with a quadratic equation’s sign (+) or (-) when it’s a positive equation, the parabola is opening up, meanwhile if it’s a negative equation, the parabola would be opening down or “reflected”. Then, the “a”-value determines the size of the parabola; whether it is stretched or compressed. We can determine if it’s stretched when the value of a is more than 1, meanwhile it would be compressed when its value is less than 1. Furthermore, the “p” represents the x-value of the vertex as well as the axis of symmetry. Lastly, the value of “q” is the y-value of the vertex.

We wanted to get enough information to be able to graph accurately that’s why we have more than one equation in order to get information in which each of these equations below show what information it can give:

Vertex/Standard Form: + q = y

with this form, this will give us the vertex (p,q) , whether it’s opening up or down (sign is positive or negative), its stretch value (a-value). However, it doesn’t give us the value of y – intercept.

General Form: + bx + c = y

With this form, it gives us the stretch value through the “a” value. Also, this form gives us the y-intercept through “c”.

Factored Form: a(x-x1)(x-x2) = y

With this form, it gives us the two x-intercepts on the graph.

We learned how to convert one form of equation to another so we are able to get information when we are asked to graph as we want to make the graph as accurate as possible.