Quadratic equations can take many different forms. There are three that we learned in this unit. Standard (Sometimes named Vertex) form, General form, and Factored form.

For this unit, the Standard form is generally (Heh.) the most useful, as it can show the most amount of information. The scale, whether it’s minimum or maximum, left/right/up/down translations, and the location of the vertex. That’s a lot. The Standard form is . I go into more detail regarding the Standard form in my last week post here.

From the standard form, you can go back into the general form by distributing and then simplifying the equation. Treat it like a normal question and eventually, you’ll reach the General form. (NOTE: You cannot go from the Standard form to Factored form. To get from Standard to Factored, you must go Standard->General->Factored.)

The General form is one of the more familiar forms you’re probably used to prior to this unit. The general form can tell us the scale, whether it’s minimum or maximum, and the y-intercept. a is the scale and whether the parabola opens up or down. c represents the y-intercept. However, the middle term, b is almost useless to us. b is a combination of the parabola translating left/right and up/down. It’s hard for us to do anything with it, so it’s disregarded for this unit. The General form is , just to refresh your memory.

From the General form, you can go to the Standard form by completing the square. To go to factored form, simply factor the equation.

The Factored form is unique, as it is the only form to tell us our roots, or x-intercepts. It can also tell us our scale, and whether the parabola opens up or down. x1 and x2 represents our roots/x-intercepts. The Factored form is .

i don’t know how to do subscript please forgive me.