Monday, March 23, 2009

A2 5.4 Completing the Square

Scribe: Ari Paez 3/23/08

How do you slove for quadradtic equations:
1. Factoring
2. Graphing
3. Setting quadratic equation to zero and solving it.

HOMEWORK QUESTIONS
# 59 on 5.3

3x^2-5x=2
Subtract the two on both sides
3x^2-5x-2=0
a= 3 b=-5 c=-2
Do box method
1. put the a term in first box and in the diagonal box put the c term
2. multiply a X c-----> 3 X -2 = -6
3. find two numbers that multiply to each other to get -6 and add up to each other to get -6 and add up to each other to get b
Answer: -6 X 1= -6 and add up to each other to get -5

3x^2

-6x
1x
-2
4. find the greatest common factor
GCF for first two boxes on top ------>
-3x^2 and -6x is 3x
-then the second boxes----->1x and -2 is 1
- after find the GCF for the first columns
3x^2 and 1x is x
-then the second to columns----->
-6x and -2 is -2
5. The factor form of this is and set it to zero and solve
(3x+1)(x-2)=0
3x+1=0 or x-2=0
x= -1/3 x=2

5.4 Completing the Square

Completing the square: forces any quadratic expression to factor.
* used to solve quadratic equations.
* used to put quadratic equations into vertex form.
- vertex form is used to slove quadratic equations that are hard to factor

To Complete a Square: Ex. 1 x^2+ 6x-16=0

Step 1. move constant term (c) x^2+6x=16
to one side and every other term to the other

Step 2. factor out the leading coefficient "a" 1(x^2+6x)= 16
* will be more relevant when a ≠1 *

Step 3. Add (1/2 X b)^2 to side with a term 1(x^2 +6x (6/2)^2) =16 +1(6/2)^2
and b term.
* add a(1/2 X b) to side with constant term (c) (x^2+6x+9) = 16+9
* simplyfiy (x^2+6x+9)=25

Step 4. factor side with a and b terms (x+3) (x+3)=25
(x+3)^2=25


HW do x^2+8x=11






10 comments:

  1. Ari is there a google doc for this? Can you share it with the class? Who is the next scribe?

    ReplyDelete
  2. the next scribe is kelsey and the google doc is on madeline's google account

    ReplyDelete
  3. This comment has been removed by the author.

    ReplyDelete
  4. is the answer (x+4)^2=27 or the square root of 11???????

    ReplyDelete
  5. the work for the problem is

    x^z+8x+11
    1.x^2+8x=-1(because you subtract the c term from both sides)
    2.1(x^2+8x)=-11(because you factor out a(or the leading coefficient))
    3.1(x^2+8x+(8/2)^2)=-11(8/2)(because you add (1/2*b)^2 tot he side with a and b, then you add it to the side with the constant term or c)
    4.(x^2+8x+16)=-11+16(because you simplify)
    5.(x+4)(x+4)=5(because you factor the new equation)
    6.(x+4)^2=5

    and that how i did it i think its right and hope it helps if you are having trouble

    ReplyDelete
  6. x^2+8x+11 is the original problem

    ReplyDelete
  7. This comment has been removed by a blog administrator.

    ReplyDelete
  8. This comment has been removed by a blog administrator.

    ReplyDelete
  9. This comment has been removed by a blog administrator.

    ReplyDelete
  10. I also wrote that the equation was x^2+8x+11. And got the same factored form. But i think its important to say that the problem is not done. You still have to solve for X.(you will get a + and - for your answers)

    ReplyDelete

Note: Only a member of this blog may post a comment.