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Quadratic And Roots

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Quadratic And Roots

1. 1. Quadratics and Roots By Petrain King IMaST Lead Coach LAUSD Modified from a PowerPoint by Mark P of the same title http://subjectsearch.wikispaces.com/Math
2. 2. Chapter 13-4 of Prentice Hall <ul><li>What are quadratic equations? </li></ul><ul><li>Solving Quadratic Equations for ROOTS. </li></ul><ul><li>How many solutions? </li></ul>
3. 3. What are quadratic equations? <ul><li>Any equation of the form: </li></ul><ul><ul><li>y=ax 2 +bx + c </li></ul></ul><ul><li>The highest power of the variable is: </li></ul><ul><ul><li>2 </li></ul></ul>
4. 4. Roots Where are they in this example?
5. 5. Roots Where are they in this example? X= Time
6. 6. Roots Where are they in this example? X= Time Y= Height Root Root
7. 7. What do quadratic equations look like? <ul><li>The name for the graph of quadratics is a: </li></ul><ul><ul><li>parabola </li></ul></ul><ul><li>If the x 2 term is positive the “bowl” opens : </li></ul><ul><ul><li>upward </li></ul></ul><ul><li>If the x 2 term is negative the “bowl” opens: </li></ul><ul><ul><li>downward </li></ul></ul>
8. 8. What do quadratic equations look like? <ul><li>If the x 2 term is positive </li></ul><ul><li>If the x 2 term is negative </li></ul>
9. 10. Example One; Page 590 <ul><li>5x 2 -8x= -3 </li></ul>5x 2 -8x+3=0 5x 2 -8x= -3 5x 2 -8x = 3 +3 +3 -3+3=0
10. 11. 5x 2 -8x+3=0 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul>5 -8 3 5x 2 -8x+3=0 A B C
11. 12. 5x 2 -8x+3=0 A B C <ul><li>-b±√b 2 -4ac </li></ul><ul><ul><ul><ul><li>2a </li></ul></ul></ul></ul>
12. 13. 5x 2 -8x+3=0 a b c <ul><li>-b±√b 2 -4ac </li></ul><ul><ul><ul><ul><li>2a </li></ul></ul></ul></ul><ul><li>-(-) 8 ±√- 8 2 -4( 5 )( 3 ) </li></ul><ul><ul><ul><ul><li>2( 5 ) </li></ul></ul></ul></ul>
13. 14. 5x 2 -8x+3=0 a b c <ul><li>-b±√b 2 -4ac </li></ul><ul><ul><ul><ul><li>2a </li></ul></ul></ul></ul><ul><li>-(-) 8 ±√ 8 2 -4( 5 )( 3 ) </li></ul><ul><ul><ul><ul><li>2( 5 ) </li></ul></ul></ul></ul>Be careful Be very careful
14. 15. <ul><li>8 ±√- 8 2 -4( 5 )( 3 ) </li></ul><ul><ul><ul><ul><li>2( 5 ) </li></ul></ul></ul></ul><ul><li>8 ±√- 8 2 -4( 15 ) </li></ul><ul><ul><ul><ul><li>10 </li></ul></ul></ul></ul><ul><li>8 ±√64 - 60 </li></ul><ul><ul><ul><ul><li>10 </li></ul></ul></ul></ul>
15. 16. <ul><li>8 ±√ 8 2 -4( 5 )( 3 ) </li></ul><ul><ul><ul><ul><li>2( 5 ) </li></ul></ul></ul></ul><ul><li>8 ±√64 - 60 </li></ul><ul><ul><ul><ul><li>10 </li></ul></ul></ul></ul>The given 4 was multiplied with a and c The given 2 was multiplied with a
16. 17. <ul><li>8 ±√64 - 60 </li></ul><ul><ul><ul><ul><li>10 </li></ul></ul></ul></ul><ul><li>8 ±√4 </li></ul><ul><ul><ul><ul><li>10 </li></ul></ul></ul></ul>10 The difference between -60 and +64
17. 18. <ul><li>8 ±√4 </li></ul><ul><ul><ul><ul><li>10 </li></ul></ul></ul></ul><ul><li>8 ± 2 </li></ul><ul><ul><ul><ul><li>10 </li></ul></ul></ul></ul>10 What’s the square root of 4? 10 0.8 ± 0.2
18. 19. 0.8 ± 0.2 <ul><li>0.8 + 0.2 = 1.0 </li></ul>0.8 - 0.2 = 0.60 The Solution ARE 1 and 3/5 6/10 = 3/5= 0.6
19. 20. Quiz Time <ul><li>2x 2 = 4-7x </li></ul><ul><li>3x 2 - 8 = 10x </li></ul>
20. 21. Homework <ul><li>Page 593 </li></ul><ul><ul><li>Problems 1-3, 7-12, 15-18 </li></ul></ul>
21. 22. Using Quadratic Equations. One example <ul><li>The path of a baseball thrown into the air can be described by this quadratic: </li></ul><ul><ul><li>h = -16x 2 + 10x + 3 (h=height, t=time) </li></ul></ul><ul><li>Using this equation, we can find the height of the ball after any amount of time by substituting a “t” value into the equation and solving. </li></ul>
22. 23. Solving Quadratic Equations. <ul><li>To solve the quadratic equation for x we must use the Quadratic Formula. Have you memorized it yet? </li></ul><ul><ul><li>x = -b ± b 2 - 4ac 2a </li></ul></ul>
23. 24. How many solutions? <ul><li>A quick way to find out how many solutions a quadratic has, simply find the value of the discriminent. </li></ul><ul><ul><li>If b 2 -4ac > 0 the are 2 solutions </li></ul></ul><ul><ul><li>If b 2 -4ac = 0 there is only 1 solution </li></ul></ul><ul><ul><li>If b 2 -4ac < 0 there are no solutions. Why? </li></ul></ul><ul><ul><ul><li>We can’t evaluate the square root of a negative number. </li></ul></ul></ul>