Math-3 Lesson 2-5 Quadratic Formula

Transcription

1 Mth- Lesson - Qudrti Formul

2 Quiz 1. Complete the squre for: 10. Convert this perfet squre trinomil into the squre of inomil: 6 9. Solve ompleting the squre: 0 8

3 Your turn: Solve ftoring

4 How would ou omplete the squre on the following trinomil? See if ou n do it. 8 We need led oeffiient = 1. 8 ) ( Add/sutrt, group the perfet squre trinomil ) ( DO NOT omine - nd /.

5 8 ( ) Multipl ( ) Distriutive propert ( ) 8 ( )

6 Complete the squre We need led oeffiient = ) 6 ( Add/sutrt 9, group the perfet squre trinomil 9 ) ( Squre of inomil

7 18 ( ( ( ) ) ) Multipl Distriutive propert ( ) 9

8 18 ( ( ( ) ) ) Multipl Distriutive propert ( ) 9

9 How would ou omplete the squre on the following trinomil? See if ou n do it. 1 Add/sutrt ( ) 1 1 ( ) 1 group Squre of inomil

10 Find the zeroes ompleting the squre. 1 ( ) 1 Set = 0 1 ( ) Isolte the squre 1 Tke squre root (don t forget +/-) 1 Simplif nd solve

11 Tod Strting with generlized stndrd from qudrti eqution, we will derive formul to find vlues of tht result in = 0. To do this we will omplete the squre. Some mth tehers require students to e le to do this.

12 Complete the Squre: Whih of the letters re vriles? nd Chnge the eqution to show tht we re finding -interepts. 0 Chnge the eqution so tht the oeffiient of orret numer for perfet squre trinomil. 0 is the

13 Isolte the terms tht ontin the vrile on one side of the equl sign then omplete the squre.. 0

14 Convert the perfet squre trinomil into the squre of inomil. Solve for undo the squre

15 Solve for This is the qudrti formul! (But it s n UGLY version of it).

16 Get rid of the prentheses under the rdil Comine rdind into single frtion.

17 I like this version the est! But it is usull written s: Simplif this: Simplif this:

18 Voulr Qudrti Formul: gives the solutions (-interepts) to ANY qudrti eqution in stndrd form. = = =

19 Your turn: Identif nd for eh of these stndrd form qudrti equtions. 7 10

20 Wht if it s not in stndrd form? Use mth properties to get it into stndrd form (sme thing left/right, omine like terms, et.) 0 =? =? =? = = - = -

21 Your turn: 0 Determine the following vlues: =?, =?, =? 1 1

22 = 1 = = Using the Qudrti formul? Identif,, nd in the stndrd form eqution. Think of - s [()()] Reple the,, nd with prentheses!!! ( ( ) ) ( ) ( ( ) )( ) Put the numeril vlues of,, into the prentheses.

23 Cn ou simplif the formul? () (1) 9 8 () Simplif the eqution. 1 [(1)()] (1) 1 = = - 1 If ou use the qudrti formul nd the solutions re nie, ou ould hve solved ftoring more esil.

24 = 1 Solve using the Qudrti formul. 1 = = 1 () (1)(1) ( ( ) ) () (1) ( ) ( ( ) (1) 1 )( ) If the qudrti CANNOT e ftored, the solutions re ugl.

25 Rememer solving ompleting the squre? 1 ( ) 1 Set = 0 1 ( ) Isolte the squre 1 Tke squre root (don t forget +/-) 1 Simplif nd solve

26 = 1 ( ( 6 = -6 = ) ) ( 6) (1) ( ) ( 6) ( ( (1) ) )( ) (1)()

27 = 1 Goth prts of the formul. 1 1 = -1 = -1 ( 1) If ou don t use the prentheses, it would e es to write this s 1 With the prentheses, -(-1) simplifies to +1!!! ( 1) (1) (1)( 1) If ou don t use the prentheses, it would e es to write this s insted of (1) 1 ( 1) 1

28 Goth prts of the formul. ( 1) ( 1) (1) (1)( 1) It is es to mke mistkes with the negtives. If ou use prentheses, then ou n tpe the epression under the rdil into our lultor nd it will e orret. ( 1) (1)( 1) 9 1 9

29 Use the qudrti formul to solve: 16 Whih of the following equtions n ou solve using the qudrti formul? ) ) ( ) 7 ) ( )( d) )

30 Your turn: Use the qudrti formul to solve: Does this prol tull ross the -is? Wht hppened in the qudrti formul so tht there ws onl imginr -interepts?

31 Whih of the following will hve imginr -interepts? (1) (1) (1) (1) (1)() 1 (1) (1)( ) (1) ( 0)

32 Whih of the following will hve onl one -interept? (6) (1) (6) (1) (1)(9) () (1) () (1) (1)(9)

33 Your turn Solve using the qudrti formul: Is this esier thn solving ftoring? 0 ( )( 1), 1