Factoring -_-
hiiii.. helloo fellow peers as you all know i am roxanne and unfortunately i'm the next scriber (thumbs down)today's class we learned how to factor perfect squares
REVIEW:
1. X²+2x+1 = (x+1)²
2. X²-2x+1 = (x-1)²
3. X²+4x+4 = (X+2)²
4. X²-4x+4 = (X-2)²
as you can see there is a pattern which is to divide the middle term by 2 then square it to get the final term of the equation
example.
X²+6X+9 --> middle term is 6x therefore you must divide it by 2 which will equal to 3. second step is to square it, which will then equal 9
REMEMBER: final term is always positive
COMPLETING A SQUARE
the equation will look like this:
y = ax²+bx+c but must be converted to y = a(x-h)²+k form
- to complete this, you must find the middle term, divide by 2, then square it
- just like the pervious questions above
example ONE.
y = x²+4x-5 convert into a(x-h)²+k form
1st step: rewrite question to y = x²+4x+ _____ -5
2nd step: find the final term by dividing the second term (4) by 2 then squaring it.
4/2 = 2² --> 4
y = x²+4x+ __4___ -5 -4
REMEMBER: what you do on one side you must do to the other side therefore you must subtract 4 on the other side.
3rd step: factor x²+4x+4 then solve the other part of the equation which is -5-4
final answer: (x+2)²-9
now you can find the:
vertex: (-2, -9) ---> (h,k)
A0S: x = -2
Domain = (-00, 00)
Range = [-9, 00)
example TWO
when there is a coefficent infront of the X² you must factor it out.
y = 3x²-12x+16
1st step: rewrite to 3x²-12x ____ +16
factor out the 3 so it will look like this
3(x²-4x+____ ) +16
2nd step: find the final term by dividing the second term (-4) by 2 then squaring it
-4/2 = (-2)² --> 4
3(x²-4x+__4__ ) +16-12
REMEMBER: what you do on one side you must do to the other side
since you're multiplying 3 by everything in the brackets, you must multiply 3 by 4 which gives you 12
therefore you must SUBTRACT 12 from 16
3rd step: factor what is in the brackets (x²-4x+4) then solve 16-12
final answer: 3(x-2)²+4
vertex: (2, 4)
AOS: x = 2
Domain: (-00, 00)
Range: [4, 00)
example THREE
When dealing with FRACTIONS, use the same steps to find the answer
y = -2x²-5x+3
1st step: factor out the -2, since you cannot factor -2 from 5 you must put it into fraction form (5/2)
-2(x²+5/2 _____ ) +3
2nd step: find final term by dividing 5/2 by 2 then squaring it.
5/2 x 1/2 = (5/4)(5/4) --> 25/16
-2(x+5/2+ __25/16___ )+3+50/16
-2(x+5/2+ ___25/16__ ) +3+ 25/8 (reduced)
REMEMBER: what you do on one side you must do to the other and since you're multiplying everything in the brackets by 2 you must multiply 25/16 by -2 then ADD it to the +3
3rd step: factor what is in the brackets which will give you -2(x+5/4)² +24/8+ 25/8
(the 5/4 came from what you figured out when you multiplied 5/2 by 1/2)
final answer: -2(x+5/4)x²+49/8
vertex: (-5/4, 49/8)
AOS: x = -5/4
Domain: (-00, 00)
Range: [-00, 49/8)
woott i'm done (: well i'm pretty sure i'm done lol if there are any mistakess please edit LOL hahaaa
i hope i did this right. kaaay anywayss NEXT SCRIBER WILLL BEEEEE ELVENN! MUAHAHAHA
posted by roxee @ 7:47 PM
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