9 1 Solving Quadratic Equations by Finding Square
9. 1 Solving Quadratic Equations by Finding Square Roots
Perfect Squares Just a reminder of the perfect squares from 1 to 20. 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400
Square Roots ¡ All positive real numbers have two square roots. l l l 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”
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400
Zero and Negative Square roots Zero has only one square root…zero. ¡ Negative numbers have no real square roots. ¡ l If you see a negative inside the square root, your answer is undefined.
Irrational Numbers ¡ ¡ Irrational numbers are numbers that cannot be written as the quotient of two integers. Irrationals are neither terminating or repeating. l l ¡ 1. 1211211112… Pi = 3. 1415…. Any square root that is not a perfect square is irrational.
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. ¡ ±
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.
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. ¡
To solve… To solve isolate the term, then take the square root of both sides. ¡ Example ¡
To solve… To solve isolate the term, then take the square root of both sides. ¡ Example ¡
To solve… To solve isolate the term, then take the square root of both sides. ¡ Example ¡
To solve… To solve isolate the term, then take the square root of both sides. ¡ Example ¡
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.
Number of solutions ¡ If = + #, then 2 solutions. = 0, then one solution… 0. = - #, then no real solution.
Example ¡ Solve
Classwork ¡ Page 507: #23 -38 and 54 -68
- Slides: 30
