L3.+Solve+quadratic+equations+using+graphs,+tables,+factoring,+algebraic+techniques,+and+the+quadratic+formula.

**1. What you need to understand.**

 * You need to understand how to solve quadratic equations a variety of ways. Solving a quadratic equation means finding what value(s) the variable must be to make the equation true. These values are called solutions.
 * Quadratic equations are equations (so there is an = sign in there) that have one variable (for example, just x, not x and y) and that has an x 2 term. It could also have an x term (linear term), and a number on its own (constant term). Some examples and non-examples are:
 * The above examples are all quadratic equations written in Standard Form. Quadratic equations can also be written in Factored Form. While there is an x 2 term in Factored Form, it is hidden. To find it you must multiply the factors together, multiplying an x by another x to get x 2.
 * You usually get two solutions with quadratic equations, but you might only get one solution (the same solution twice) or no solutions.
 * The following chart shows many of the ways to get from a quadratic equation (either in Standard Form or Factored Form) to the solutions (either 2,1 or none). The arrows are numbered and described below.


 * 1) Use your calculator to graph y=(x+3)(x-2)
 * 2) (see Standard N for more details) Find where your graph crosses the x-axis (the x-intercepts). When you change the signs of these intercepts you get the values after the x's inside the parentheses.
 * 3) (see Standard N for more details) When you change the signs of these solutions you get the values after the x's inside the parentheses.
 * 4) (see Standard N for more details) Factor the equation. You can this using the 'box method'.
 * 5) (see Standard N for more details) Expand the equation. You can also use the box method, but FOIL, or the smiley face method also work.
 * 6) Use your calculator to graph y=x 2 + x - 6
 * 7) Find where your graph crosses the x-axis (the x-intercepts). These x values are the solutions. (See Example 5 below)
 * 8) (see Standard N for more details) The solutions are the x-intercepts. You'll need more information (another point) to figure out the rest of the quadratic graph.
 * 9) Set each factor (each bit in parentheses) equal to zero. Then you split the equation in two and solve each part separately. (See Example 1 below)
 * 10) Use algebraic techniques, or the Quadratic Formula if you have all three terms. (See Examples 2, 3 and 4 below)

You can also use tables to find the solution(s) by looking for the x values when y=0.

**2. Example Problems.**
Example 1

Example 2

Example 3

Example 4

Example 5 The solutions for this graph are x = 2 and x = 6.

3. Common mistakes or misunderstandings.
//[MrB: Elaborate and explain each of these bullets more.]//
 * Algebraic errors
 * Arithmetic errors
 * Forgetting one of the solutions
 * Sign errors
 * Not using the quadratic formula correctly

4. For more information.

 * We made our own YouTube videos that described how to solve either Example 2 or Example 3.
 * These are links to other videos that show:
 * Solving using the Factored Form
 * Solving using square roots
 * Solving using the Quadratic Equation
 * Solving using graphing
 * The Core-Plus 2 text book: Unit 5 Lesson 1 (pages 326-358)
 * This might help you remember the quadratic formula (if you don't die of embarrassment first)
 * This website has some good worked examples in a non-video format.