Lesson 10

Lesson 10 - Lesson 10 Quadratic equation an equation of the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lesson 10 Quadratic equation: - an equation of the form are real numbers and - special forms of quadratic equations: , where and The degree of a quadratic equation is ________ Example 1: Determine whether each of the following equations is quadratic. a. b. c. d. ) e. ( f. g. In order for an equation to be quadratic, the degree must be _________. Example 2: If , what must be true about and ? Example 3: If , what must be true about , and ? Zero Factor Theorem: - the product of two or more factors is zero if and only if at least one of the factors is zero if and only if or if and only if , or Does this work for any values other than zero ( or Why not? )? Why Solving an equation by factoring: 1. write the equation in polynomial form and set it equal to zero 2. factor 3. use Zero Factor Theorem Example 4: Solve the following equations by factoring: a. ) b. ( c. d. e. Is there another way to solve parts d. and e.? If get just , what could we do to both sides of the equation to by itself? √ √ Special Quadratic Equation: - to solve an equation that involves a perfect square, take the square root of both sides - this can be used for a single term that is a perfect square, or a quantity that is a perfect square - if , then √ ) - if ( , then √ and √ Do we have to include the sign? Why or why not? Example 3: Solve the following equations by taking the square root of both sides a. b. ( c. ( ) ) d. ( ) Why is it that if ? √ , then , but if , then We’ve seen how to solve quadratic equations which are factorable and quadratic equations which are perfect squares, but what about quadratic equations which are neither? If a quadratic equation is not factorable and is not a perfect square, how do we solve it? Quadratic equations which are not factorable and are not perfect squares can be changed into perfect squares by using a procedure called completing the square. Examples of Perfect Squares: ( ) ( )( ( ) ( ) ( ) ( ) ( ) ) When a perfect square is in quadratic form, do you notice a relationship between the coefficient of the middle term and the constant term? The constant term is always half the coefficient of the middle term squared. ( ) ( ) ( ) ( ( ) () ( ) ) () ( ) ) ( ( ( ) ) Using the pattern from the previous examples, how can we make a quadratic equation such as a perfect square? Completing the square: Given a quadratic equation of the form that is not factorable, 1. divide each term by the leading coefficient ( ) 2. isolate the constant term ( ) 3. add the square of half the coefficient of to both sides () 4. solve using the special case ( If the leading coefficient is 1 ( √) ), skip the first step. Example 4: Solve the following equations by completing the square: a. b. c. ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online