Description

At the end of this subject, we learn how to solve the next level of polynomial equations after linear equations, the quadratic equations. We learn multiple ways of solving quadratic equations such as by factoring and the square root method; solving quadratics equations by completing the square and by using the Quadratic Formula. We also explore complex numbers and solving quadratic equations with complex number solutions as well as graphing the parabola and applications of quadratic equations to real world scenarios.

Sections of this topic include:

1. Solving Equations by Factoring and the Square Root Method

   The first several methods of solving quadratic equations is to solving by either factoring a polynomial and using the zero factor property or by using the square root method. Groups in this section include solving factored equations; solving quadratic equatinos by factoring; solving quadratic equations using the square root method.

2. Solving Quadratic Equations by Completing the Square

   Another way to solve quadratic equations is by using the method of completing the square. Groups in this section include completing the square; and solving by completing the square.

3. Solving Quadratic Equations by the Quadratic Formula

   The final way of solving quadratic equations is by using the quadratic formula. Groups in this section include substituting a,b, and c into the quadratic formula and simplifying; solving quadratic equations by the quadratic formula; solving quadratic equations by factoring, by the square root property, or the quadratic formula.

4. Solving Quadratic Equations with Complex Number Solutions

   In solving quadratic equations using the quadratic formula, it is possible to square root negative numbers. To this end, we explore complex numbers and their role as solutions to quadratic equations. Groups in this section include simplifying radaicans containing negative numbers; adding or subtracting complex numbers; multiplying complex numbers; dividing complex numbers; solving quadratic equations using the square root method with complex number solutions; solving quadratic equations using the quadratic formula with complex number solutions.

5. Graphing Quadratic Equations; The Parabola

   The question arises about what the graph of a quadratic equation may look like? We explore this question with the idea of how to graph parabolas. A Group in this section is skietching the graph of an equation by making a table of ordered pairs with given x values.

6. More Applications

   In this final section, we explore how to apply quadratic equations to real world scenarios.