# Quadratic Functions: Standard Form

- Author:
- Whit Ford

Standard Form of the equation of a parabola is used often, as it is what you end up with after multiplying two binomial factors together, then simplifying.
The coefficients of each term in Standard Form,

**a**,**b**, and**c**, are required when using the Quadratic Formula to find the*x*-intercepts of the graph of a parabola. The graph below contains three green sliders. Click on the circle in a slider and drag it to the left or right, while watching the effect it has on the graph.Once you have a feel for the effect that each slider has, see if you can adjust the sliders so that:
- the vertex lies to the right, or left, of the

*y*-axis - the vertex lies above the*x*-axis - the graph becomes a horizontal line, or opens down - some part of the graph passes through the blue point on the graph: (-3, -1) - the vertex of the graph (the blue point labelled V) passes through the blue point on the graph: (-3, -1). This is much more challenging!**a**is referred to as the "dilation factor". It determines how much the graph is stretched away from, or compressed towards, the*x*-axis. Note what happens to the graph when you set**a**to a negative value.**c**shifts (translates) the graph vertically.**b**alters the the graph in a complex way. How would you describe the effect that changing the value of**b**has on the graph? If you wish to explore this behavior in a bit more depth, you may use this applet: http://tube.geogebra.org/material/simple/id/648429. These three values,**a**,**b**, and**c**, will describe a unique parabola. To completely describe any parabola, all someone needs to tell you are these three values. However, there are also other ways of describing everything about a parabola that may be a bit more intuitive. If you wish to use other applets similar to this, you may find an index of all my applets here: https://mathmaine.com/2010/04/27/geogebra/