### November 14th 2021 archive

In week 10 of my precalc 11 class, we learned about three different forms of equations that can be graphed, and how to convert them from one to another. Here are the different forms (with examples below):

General Form: y = ax² + bx + c

y = x² – 2x + 4

y = -2x² + 5x -16

Standard or Vertex Form: y = a(x – p)² + q

y = (x – 4)² + 7

y = 3(x – 2)² – 1

Factored Form: y = a(x – x₁)(x – x₂)

y = 2(x + 7)(x – 3)

y = (x – 5)(x – 2)

Each of these equation types can show different things about what the graph will look like. For example, the last number (with no variable) in general form tells you the y-intercept. The 2 numbers after the x in factored form are the roots of the equation (make sure to change the signs first). In order to fully graph a quadratic equation, sometimes you need to convert one form of the equation into another. Here is how to convert general form into factored or standard:

This is how to change standard/vertex form into general or factored:

Finally, here is how to convert factored form into general or standard: