Algebra: Chapter 13, Lesson 1, page 576.
Introduction to Quadratic Equations
An equation that can be written in the form of `ax^2 + bx + c = 0` is a quadratic equation. This is the “standard form”. The solutions of the quadratic equation are called the:
- roots
- solutions
- x-intercepts
- answers
We can factor the equation and use the zero product property to find its solutions. There can be `0`, `1` or at most `2` solutions. This is because we have an exponent with power 2 (the `ax^2` term).
1. Equations of the form `ax^2 + bx = 0`
can be factored by taking out an `x` leaving us with `x(ax + b)` and using the zero product property we have `x = 0` and `ax + b = 0` as solutions.
2. Equations of the form `ax^2 + bx + c = 0`
can factored using the BOX METHOD with solutions again arrived at by using the zero product property.
Remember too, the inflexion point (the vertex, the point where the slope of the parabola changes direction) is `-b/(2a)`. This can help with the graph if you need to make one.
Purplemath has this link that is pretty good with more explanations and review.