1. 9.1 Solving Quadratic Equations by Finding Square Roots

2. Perfect Squares Just a reminder of the perfect squares from 1 to 20. 1121 4144 9169 16196 25225 36256 49289 64324 81361 100400

3. 1121 4144 9169 16196 25225 36256 49289 64324 81361 100400

5. Square Roots  All positive real numbers have two square roots. A positive square root A negative square root Example 6*6=36 and -6*(-6)=36 Say “square root of 36 is plus or minus 6”

6. 1121 4144 9169 16196 25225 36256 49289 64324 81361 100400

7. Zero and Negative Square roots  Zero has only one square root…zero.  Negative numbers have no real square roots. If you see a negative inside the square root, your answer is undefined.

8. Irrational Numbers  Irrational numbers are numbers that cannot be written as the quotient of two integers.  Irrationals are neither terminating or repeating. 1.12112111211112… Pi = 3.1415….  Any square root that is not a perfect square is irrational.

9. Radical Expressions  Radical expressions involve square roots.  The square root symbol is a grouping symbol.  Operations inside a radical symbol must be performed before the square root is evaluated. ±

10. Quadratic Equations  A quadratic equation is an equation that can be written in the following standard form:  In standard form, a is the leading coefficient.

11. When b=0  In this section, we are going to solve quadratic equations where b=0.  So, we will be solving equations in the form.

12. To solve…  To solve isolate the term, then take the square root of both sides.  Example

13. To solve…  To solve isolate the term, then take the square root of both sides.  Example

14. To solve…  To solve isolate the term, then take the square root of both sides.  Example

15. To solve…  To solve isolate the term, then take the square root of both sides.  Example

17. Number of solutions  If equals a positive number, then there are 2 solutions.  If equals 0, then there is one solution…0.  If equals a negative number, then there is no real solution.

18. Number of solutions  If = + #, then 2 solutions.  If = 0, then one solution…0.  If = - #, then no real solution.

19. Example  Solve

20. Classwork  Page 507: #23-38 and 54-68