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 |
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
Ari is there a google doc for this? Can you share it with the class? Who is the next scribe?
ReplyDeletethe next scribe is kelsey and the google doc is on madeline's google account
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ReplyDeleteis the answer (x+4)^2=27 or the square root of 11???????
ReplyDeletethe work for the problem is
ReplyDeletex^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
x^2+8x+11 is the original problem
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ReplyDeleteI 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)
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