Intermediate Algebra Quadratic Equations Functions Inequalities

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Intermediate Algebra

9. Quadratic Equations, Functions, and Inequalities

Description

Extending our knowledge of solving linear equations, we now focus on solving quadratic equations. In this topic, we explore solving polynomial equations by factoring and the square root property; solving quadratic equations by completing the square and by using the quadratic formula; solving equations that are quadratic in form; solving inequalities involving quadratic forms; exploring variation and applications to the real world.

Sections in this topic include:

1. Solving Polynomial Equations by Factoring and the Square Root Property

We begin this section by recalling how to solve quadratic equations by either factoring and using the zero factor property or by using the square root property. Groups within this section include: solving quadratic equations by factoring; solving quadratic equations by using the square root property; writing equations given the solution; solving quadratic equations using perfect square trinomials and the square root peropty; solving four degree equations by factoring and using the square root property; solving literal equations using the square root property; and solving equations containing several variables using the square root property.

2. Solving Quadratic Equations by Completing the Square

A second way of solving quadratic equations is by completing the square. Groups within this section include: completing the square; solving quadratic equations by completing the square; solving quadratic equations by completing the square, square root property, or by factoring; solving radical functions; solving rational functions; completing the square for both x and y.

3. Solving Quadratic Equations Using the Quadratic Formula

The last way of solving a quadratic equation is by using the Quadratic Formula. Groups within this section include: using the discriminant; finding values in the discriminant to determine solutinos to a quadratic equation; writing quadratic equations given the solutions; solving quadratic equations by any method.

4. Solving Equations Involving Quadratics

Many equations can be "quadratic in form". To this end, this section investigates these types of equations and their solutions. Groups within this section include: solving higher order equations by factoring; solving sixth degree equations by factoring; solving radical equations.

5. Solving Inequalities Involving Quadratics

This section focuses on how to find intervals of solutions to inequalities that contain factorable quadratic factors in the numerator or denominator of rational expressions.

6. Variation

A useful tool in mathematics is solving applied problems using variations. These variations may be direct, inverse (indirect), or joint. Groups within this section include: writing variations in the form of an equations; solving variation problems.

7. More Applications

This section investigates applications using quadratic equations and their solutions to real world problems.

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