Standard Form and Vertex Form
Exploring both the standard form and the vertex form of the quadratic function you have been able to form some ideas about the following,
- How are they similar?
- How are they different?
- What are the benefits of each?
- Make connections to the activity with Desmos.
You may have noticed that they both have an \(a\) that determines if the parabola has the orientation of opening up or opening down, which results in a minimum or maximum, respectively.
You may have noticed that the standard form \(y=ax^2+bx+c\) that the constant \(c\) is the \(y\)-intercept. The standard form is not the most effective in graphing quickly.
You may have noticed that the vertex form, \(y=a(x-h)^2+k\) is very specific in being able to determine if the graph is translated left or right, by the \(h\) value or up or down, by the \(k\) value.
Now is an opportunity to practice and apply what you have learned in this lesson.