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1
Parabolas
Do you see a similar shape? What is it?
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Factoring
Solving Quadratics
Completing the Square
Quadratic Formula
Graphing
(PreviousChapter)
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3
Steps to Factoring
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12.1 Quadratic Equations with Perfect Squares
ax+b=0 linearequation(firstdegree)
1) Solve:
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2) 3)
4)
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5)
Notes:
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RecognizingPerfectSquares
1)
2)
3)
4)
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Examplesforyoutosolve:
1)
2)
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3)
4)
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5)
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FactoringMethod
6)
7)
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8)
9)
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10)
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Quadratic equations make parabolas. Where could we see parabolas
in real life?
http://blog.lib.umn.edu/abinf002/architecture/SL_2DGatewayArch_small.jpg
http://i1.trekearth.com/photos/83066/p17200661_bern_bridge.jpg
http://cache.rcdb.com/pictures/picmax/p6088.jpg
http://www.maxwaugh.com/images/osu04/punt.jpg
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Completing the Square
ax2+ bx + c = 01) Check to see if the bookends (a and c) are
perfect squares. If they are skip to step 6.2) Isolate the ax2 + bx
terms3) Factor out a leading coefficient if needed 4) To complete
the square find half of b and square it.5) Add the result of step 4
to both sides of the equation.6) Factor the one side.7) Solve
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12.2CompletingtheSquare
1)
2)
3)
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Solvebycompletingthesquare
4)
5)
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6)
7)
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8)
9)
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Quadratics can be used in dealing with problems involving
physics.
SirIssacNewton
Careers using
quadraticsEngineeringWelding/FabricationScientist
RocketbeinglaunchedWhenwillithittheground?
Weusetheformulastosolvefortheamountoftimeanobjectwillbeintheairorwhenitwillhittheground.
Whenwilltheballhittheground?http://clubdir.gaa.ie/clg/tipperaryinstitute/images/dwyer%20kicking%20to%20touch.JPG
Clickhere
http://climateprogress.org/wpcontent/uploads/2008/05/newton_16431727.jpg
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Ch12.3TheQuadraticFormula
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Solveforthevariable:
1)
-bb2-4ac2a
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-bb2-4ac2a
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3)
4)
-bb2-4ac2a
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5)
6)
-bb2-4ac2a
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7)
-bb2-4ac2a
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Chapter12Review
1.) 2.)
3.) 4.)
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Solvebycompletingthesquare:
5.)
6.)
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7.) 8.)
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Solvebyusingthequadraticformula:
9.) 10.)
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11.) 12.)
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Attachments
9.4Lab.doc
9.4 Applying Quadratic Equations Lab
Many of the real-world problems you solved in Chapters 8 and 9
were physical problems involving the path of an object that is
influenced by gravity. These paths, called trajectories, can be
modeled by a quadratic function. The formula relating the height of
the object H(t) and time t is shown below.
2
0
1
()
2
Htgtvth
=-++
H = height of object
g = Acceleration due to gravity (9.8 m/sec
2
or 32 ft/sec
2
)
v
0
= initial velocity of the object
h = initial height of the object
Ex) Juan kicks a football at a velocity of 25 meters per second.
If the ball makes contact with his foot 0.5 meter off the ground,
how long will the ball stay in the air?
Ex) Katharine is on a bridge 12 feet above a pond. She throws a
handful of fish food straight down with a velocity of 8 feet per
second. In how many seconds will it reach the surface of the
water?
1) Darren swings at a golf ball on the ground with a velocity of
10 feet per second. How long was the ball in the air?
2) Amalia hits a volleyball at a velocity of 15 meters per
second. If the ball was hit from a height of 1.8 meters, determine
the time it takes for the ball to land on the floor. Assume that
the ball is not hit by another player.
3) Michael is repairing the roof on a shed. He accidentally
dropped a box of nails from a height of 14 feet. How long did it
take for the box to land on the ground? Since the box was dropped
not thrown, v
0
= 0.
4) Carmen threw a penny into a fountain. She threw it from a
height of 1.2 meters and at a velocity of 6 meters per second. How
long did it take for the penny to hit the surface of the water?
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_1269172093.unknown
_1269171946.unknown
SMART Notebook
Page 1: Mar 18 - 5:56 PMPage 2: Ways to solvePage 3: Factoring
StepsPage 4: Jan 31-1:37 PMPage 5: Jan 31-1:42 PMPage 6: Jan
31-1:43 PMPage 7: Jan 31-1:44 PMPage 8: Jan 31-1:46 PMPage 9: Jan
31-1:47 PMPage 10: Jan 31-1:48 PMPage 11: Jan 31-1:48 PMPage 12:
Jan 31-1:49 PMPage 13: Jan 31-1:49 PMPage 14: Feb 13-8:54 AMPage
15: Real-life picturesPage 16: Feb 15-8:26 AMPage 17: Steps to
complete the squarePage 18: Jan 31-1:50 PMPage 19: Jan 31-1:51
PMPage 20: Jan 31-1:52 PMPage 21: Jan 31-1:52 PMPage 22:
Applications of QuadraticsPage 23: Jan 31-1:54 PMPage 24: Quadratic
FormulaPage 25: Jan 31-1:55 PMPage 26: Jan 31-1:56 PMPage 27: Feb
1-9:51 AMPage 28: Feb 1-9:52 AMPage 29: Feb 1-9:52 AMPage 30: Feb
1-9:53 AMPage 31: Feb 1-9:54 AMPage 32: Feb 1-10:12 AMPage 33: Feb
1-10:13 AMPage 34: Feb 1-10:13 AMAttachments Page 1
