Quadratics

The Quadratics Unit Involves;
Factoring, writing, and solving quadratic equations.
Factoring types: Greatest Common Factor (GCF)
Difference of Two Squares
Sum or Difference of Perfect Cubes
Factor by Grouping and
Trinomial Factoring
All of the methods are used to solve quadratic equations except sum or difference of cubes (we use these to solve polynomial functions in a later unit)
Generally, quadratic equations are written in two ways;
Standard form y = ax2 + bx + c or
Vertex form y = a(x - h)2 + k

When it comes to solving quadratics, we have four methods;
1) Factoring
2) Complete the Square
3) Graphing and
4) The quadratic formula

Quadratics Homework #1

First Period Factoring Review and Practice

Before we get into solving quadratic equations, we take a minute to review how to simplify radical expressions. Later in this course we will get into working with radical functions but for now, we just need to know how to simplify radicals.

The following document is your homework.

Characteristics of Quadratics "How To" sheet.

Characteristics of Quadratics

SOLVING QUADRATIC EQUATIONS
We begin to solve quadratic equations at this point. Remember that solutions of quadratics are the points at which the graph of the quadratic (parabola) intersects the x axis. These point are called "solutions, zeros, roots, or x intercepts." They all mean the same thing, they are the solutions to a quadratic equation.
The first method we will use is solving by factoring.
Step 1 - rewrite the equation so that it equals 0 (if needed)
Step 2 - factor the polynomial completely
Step 3 - set each factor equal to 0
Step 4 - solve each factor
REMEMBER - any factor, including a GCF, that contains a variable must be set equal to 0 when solving
The short video below gives a couple of examples how this works. You might want to watch it a couple times if it helps.

Solving Quadratics by Factoring Homework 1

For two of the other methods for solving Quadratic Equations, we need to be able to simplify radicals, numbers under a square root symbol. We will use this in other areas we will be studying but we begin using radicals here in Quadratics.
In order to simplify radicals we need to break down numbers and or variables into their prime factors. In order to simplify, we need pairs of common factors. Each pair will result in one factor being taken out from under the radical and become a coefficient of the term while any single factors remain under the radical symbol. Below you will find a video that helps explain simplifying radicals.

Simplify Radicals Homework

Solving Quadratics by
Completing the Square

The next page is a video that explains how to solve a quadratic by completing the square. It is a lengthy video (a bit over 17 minutes) but does a good job of demonstrating each of the types of problems you may encounter when asked to solve by completing the square.

Below is a step by step "How to Complete the Square" instruction sheet. Use it to reinforce today's lesson.

Completing the Square Homework

Solving Quadratics by
The Quadratic Formula

Solving quadratic by graphing.
When solving quadratics by graphing, it is a calculator based solution. You can find the solution by rewriting the quadratic into standard form (if needed), type it into y1 in the graphing utility, and then graph. Once you know that the function actually has x intercepts, you can find them by;
Push 2nd & trace
Select zero (#2)
Scroll to the left side of the left most intercept and hit enter
Scroll to the right side of the left most intercept and hit enter
Hit enter a third time and the calculator will display the x intercept (solution)
Repeat this same process with the right most x intercept to find the second solution.

Solve using various methods.

Solving Quadratic Word Problems
Below you will find a document that helps explain the steps in solving a quadratic word problem. Use this in addition to the notes you took in class to help you solve the assigned problems.

Quadratic Word Problems Homework below.

Quadratics Test Review
Below you will find the Quadratics Unit Test Review. The answers follow in the next window. Please work carefully and make sure you understand how to do each type of problem. It is very important you can do these on the test.

Test Review Part 2